How should satipatthana be understood in regard to external/internal minds?

In Uddesa Vibhaṅga Sutta one of the main Suttas where the term internally and externally is analysed in detail. Analysis of what internally and externally appears multiple places. Couple quote on this is as follows, but it is best to read the whole Sutta to get a more thought out idea.

Summary

Bhikshus, a monk should examine things in such a way that while he is doing so, his consciousness is neither distracted nor scattered externally, nor slack internally; and by not clinging, would be unagitated. Bhikshus, if his consciousness is neither distracted nor scattered externally, nor slack internally;38 and by not clinging, is unagitated, then there is in him no further arising or producing of suffering, that is, of birth, decay and death.”

Internally:

Having cognized a mind-object with the mind, if his consciousness follows after the sign of mindobject, bound to gratification in the mind-object sign, enthralled by gratification in the mind-object sign, yoked to the fetter of gratification in the mind-object sign— then, the consciousness is said to be distracted and scattered externally. Thus, avuso, is the consciousness said to be distracted and scattered externally

Externally:

Having cognized a mind-object with the mind, if his consciousness does not follow after the sign of mind-object, not bound to gratification in the mind-object sign, not enthralled by gratification in the mind-object sign, not yoked to the fetter of gratification in the mind-object sign— then, the consciousness said to be distracted and scattered externally. Thus, avuso, is the consciousness said to be undistracted and unscattered externally.

Insight

He does not regard consciousness as the self, or the self as possessing consciousness, or consciousness as in the self, or the self as in consciousness. That consciousness of his changes, becoming other. When that consciousness of his changes, becoming other, his consciousness70 is not caught up with the consciousness‟s changing. No agitated mental states born of the preoccupation with that consciousness‟s changes arise together and continue to overwhelm his mind. Because his mind is not overwhelmed, he is fearful, vexed, and full of longing, and due to non-clinging, he is unagitated. Thus, avuso, is there neither agitation nor clinging.

Sorce: Uddesa Vibhaṅga Sutta.

There's a long discussion here on DhammaWheel: Satipatthana: Internal and external contemplation

It starts by saying that, according the commentarial literature (emphasis mine),

The first way of interpreting follows the Abhidhammic and commentarial literature, which interprets 'internally/externally' to encompass phenomenon arising in oneself and others. So, when one contemplates body/feelings/mind/dhammas, one contemplates them in oneself and in others. We of course cannot read the minds of others. But reading the Abhidhammic and commentarial literature, Ven. Analayo suggests that we can direct mindfulness towards the outer manifestations of others (facial expressions, posture, movements, etc) so as to practice satipatthana 'externally'.

The second way of interpretating is suggested by some contemporary teachers who interpret 'internally/externally' to refer to what is inside of the body and what is on the outside of the body--i.e. the surface of the skin. I won't reproduce Ven. Analayo's arguments in detail here. But he more or less argues that while such interpretations are not entirely unfounded and have their practical benefits, they have their limits (e.g. it becomes hard to maintain such a distinction when one begins to contemplate the dhammas).

Ven. Sujato's translation is,

And so they meditate observing an aspect of the mind internally, externally, and both internally and externally.

Iti ajjhattaṃ vā citte cittānupassī viharati, bahiddhā vā citte cittānupassī viharati, ajjhattabahiddhā vā citte cittānupassī viharati;

The word used there for "internally" is ajjhattaṃ ...

concerning oneself in oneself; inwardly, personally; in regard to oneself (opp. bahiddhā).

... (and for externally, bahiddhā), so IMO it's plausible that the opposite of "in oneself" might be "in someone else".

Here is a short quote from an article on BuddhaNet called "The Vipassana Retreat - The Six Sense-spheres". In here it's talked about how internally and externally should be understood.

The Vipassana Retreat

12. The Six Sense-spheres

The teaching of the sense-spheres is to be found in the Contemplation of Mind (dhammanupassana) in the text we are following: the Satipatthana Sutta, which by now is familiar to you as the Four Establishments of Mindfulness.

After each section in the text in the Satipathana Sutta, you will find this passage: "In this way he abides contemplating the body as a body (or feelings, mind states and mental phenomena) internally, externally, and both internally and externally". What does this mean? It means that the focus of one's attention changes from the subjective (internal) to the objective (external) and by "both" is meant the understanding of the interrelationship or interdependence.

The focus of the practice so far has been mainly introspective; now the watchfulness or attentiveness can be expanded to include the external as well. That is, the attention is switched from the subjective to the objective. This is done by orientating to the sense-spheres, which are about the relationship between oneself and the outer world. Practising both internal and external satipatthanas can prevent self-absorption, and achieve a skilled balanced between introversion and extroversion.

The importance of contemplation of the sense-spheres is that it directs awareness to the six “internal” and “external” sense-spheres and the fetters (samyojana) arising in dependence on them. Although a fetter arises dependent on sense and object, the attaching nature of such a fetter should not be attributed to the senses or objects themselves, but to the influence of the hankering pull of desire (tanha)...

The article says further on how to make an orientation to a sense-door:

Orientation to a Sense-door

To make an orientation to a sense-door, you start by literally coming to your senses - seeing, hearing, tasting, touching and smelling. These are the five sense-doors or sense bases; the 'sixth sense' is 'consciousness of something', which is the mind-base with its eye-consciousness, ear-consciousness, etc. You also need to be aware of the senses internally as well as externally. That is, the organs and their sense objects: nose/smell, tongue/taste, body/tactile objects, ear/sound, mind/mind-objects or consciousness.

Attentiveness or 'presence of mind' at one of the sense-doors during a sense impression is the way to practice. For example, most people are predominantly visual, so being attentive at the eye-door allows you to notice the effects of the contact between the eye and the visible objects and how you are relating to them.

The process is this: there is the eye (the internal base), and a visible object (the external base). With contact or a sense impression between the sense-door and external object, consciousness arises followed by feeling. The moment of consciousness ordinarily is too rapid to catch while the feeling tone can be more easily known and apprehended.

This orientation to a sense-door brings awareness of what is happening during the moment of contact or the sense impression, and with it the ability to monitor the associated feelings and consciousness that arises. When this feeling tone is apprehended, the link to liking and disliking is broken and therefore one is free at that moment from conditioned suffering.

Here is a quote from the Wiki on the 6 sense bases:

Ṣaḍāyatana (Sanskrit) or saḷāyatana (Pāli) means the six sense bases (Pāli, Skt.: āyatana), that is, the sense organs and their objects. These are:

Eye and Vision

Ear and Hearing

Nose and Olfaction

Tongue and Taste

Skin and Touch

Mind and Thought

That is, in Buddhism, the sixth "internal" and "external" sense bases are: mind (Skt., manas; Pali, mano); and, thought (along with memory and emotion) (Skt., dharma; Pali, dhamma).

Ṣaḍāyatana is the fifth link in the Twelve Nidānas of Pratitya-Samutpada (Dependent Origination) and thus likewise in the fifth position on the Bhavacakra (Wheel of Becoming). Ṣaḍāyatana (Sense Gates) is dependent on Nāmarūpa (Name and Form) as condition before it can exist.