Does this kind of meditation have grounding or an equivalent in Buddhism?

yes it is like what people who claim to be buddhists do, but since you do not force to view perception, feelings, and thoughts as impermanent, unsatisfactory and not self, which is what cultivates thoughts of renunciation, it is not the dhamma, but at least you do not claim it is the dhamma, contrary to the people who claim to be buddhists.

It is like the ''mc mindfulness" that westerner have invented and push in their companies and military, like the story about the matthieu ricard saying that militry snipers can be mindful like the buddha teach it, and claiming that their employees will improve their well being (and therefore be more productive, which is really their secret goal).

The ''Allow the aversion to be there'' is a popular view but joy and pleasure must be cultivated to reach samadhi, ie ''meditation''. What you do would be at best ''minduflness'', ie what is done before ''meditation'', but again you cannot rely on just letting things to happen, you have to prevent bad things, ie aversion, attachment , ill will and so on, and seek actively the opposites.

The popular view stems from the People infatuated with sensuality who confuse judgement and tastes : they say I like therefore ti is good or right and I dislike it therefore it is bad or wrong.

The people infatuated with sensuality who want to feel buddhist are even worse : they hear that part of the origin of suffering is ''Greed is a root of what is unskillful, aversion is a root of what is unskillful'' they turn this into ''judgement is a root of what is suffering''

And when they mix this with their obsessions with the nature of phenomena, with their obsession about what truly exists and what not truly exists, they turn their view into lack of ''the watcher'' ''the doer'' or ''the witness'' and a good meditation is when there is only awareness, ie there is no object nor subject. Because for those people when there is a judgement is when there is the object-subject duality, the ''naked awareness'' is when thoughts cannot stick to that state.

For instance, Tulku Urgyen Rinpoche proudly tries to spread his little fantasy in his famous book about dzogchen: By training thoroughly in this way, discursive thinking will gradually grow less and less, and moments of thoughtfree wakefulness will grow longer and longer. When this nonconceptual wakefulness lasts one hour, you have attained the level of an arhat. When it lasts throughout the day, you have attained the level of a bodhisattva. When it is uninterrupted day and night, you have become a fully enlightened buddha. There is nothing more precious than this.

When it comes to state what is real and unreal, they show their great lack of understanding of dependant orgination, like when they claim ''sentient beings do not see the four truths of the noble ones [F.241.a] as they really are, and therefore they do not transcend saṃsāra, which is actually unreal.” '' and ''The Bhagavān replied, “Mañjuśrī, whoever sees all conditioned states as unproduced has understood suffering. Whoever sees all phenomena as unarisen has abandoned its origin. [F.242.a] Whoever sees all phenomena as having completely passed into nirvāṇa has realized cessation. Whoever sees all phenomena as having no existence has cultivated the path.'' http://read.84000.co/translation/toh178.html They fail to understand that being conditionned does not mean non existence.

Then they again mix this with the generic popular fantasy that ''mother nature is good'' and ''everything is connected'', so when it comes to phenomena, they say that ''phenomena are already perfect'' and '' all phenomena are interdependant'', still trying to pass their view as interdepandant origination. Which quickly leads them to say that ''there are no bad thoughts or good thoughts'' and ''in fact there was nothing to change, nothing to improve to get enlightened'' so they say proudly that ''each moment is perfect the way it is, people are suffering only because they fail to see that each moment is perfect the way it is'', which has nothing to do with the dhamma.

Then they use this as a basis for their famous method ''taking the fruit as the path'', ie they cling to their fantasy that they can transform bad mental factors, in order to skip the actual cleaning of the mind thoughts by thoughts, while claiming that they are even more righteous and less intellectual than the people who directly change their thoughts.

And all of this due their cravings for sensuality, especially thoughts, which make them confuse judgement and with greed and aversion.

The next level of mediation for you would be what Nanda does

This is how Nanda guards the sense doors. If he has to look to the east, he wholeheartedly concentrates before looking, thinking: ‘When I look to the east, bad, unskillful qualities of desire and aversion will not overwhelm me.’ In this way he’s aware of the situation.

If he has to look to the west … north … south … up … down … If he has to survey the intermediate directions, he wholeheartedly concentrates before looking, thinking: ‘When I survey the intermediate directions, bad, unskillful qualities of desire and aversion will not overwhelm me.’ In this way he’s aware of the situation. This is how Nanda guards the sense doors.

This is how Nanda eats in moderation. Nanda reflects properly on the food he eats: ‘Not for fun, indulgence, adornment, or decoration, but only to sustain this body, to avoid harm, and to support spiritual practice. In this way, I shall put an end to old discomfort and not give rise to new discomfort, and I will live blamelessly and at ease.’ This is how Nanda eats in moderation.

This is how Nanda is committed to wakefulness. Nanda practices walking and sitting meditation by day, purifying his mind from obstacles. In the evening, he continues to practice walking and sitting meditation. In the middle of the night, he lies down in the lion’s posture—on the right side, placing one foot on top of the other—mindful and aware, and focused on the time of getting up. In the last part of the night, he gets up and continues to practice walking and sitting meditation, purifying his mind from obstacles. This is how Nanda is committed to wakefulness.

This is how Nanda has mindfulness and situational awareness. Nanda knows feelings as they arise, as they remain, and as they go away. He knows perceptions as they arise, as they remain, and as they go away. He knows thoughts as they arise, as they remain, and as they go away. This is how Nanda has mindfulness and situational awareness.

https://suttacentral.net/an8.9/en/sujato

but this requires energy [to do it day after day] and faith in the buddha.