How is one supposed to be compassionate and 100% free of suffering while others are suffering?

you might have just mentioned a very high level dhamma. Even compassion is a conditioned phenomenal. It is also subject to dukkha, annicca, annatta. It is unreliable. It changes. I dont remember which sutta, but those who practice compassion mediation and take note of its condition, it is possible to reach enlightenment in this life time, if not, they would appear in Bhramakayika world and become none-returner after that. If it works for you (practicing compassion meditation and take not of its unreliability), I'd say run with it.

In Buddhism, we practice Brahama Viharas. There are four Brahama Vihara and the last one is the Upekkha or equanimity. Once you understand the nature of Anocca, Dukkha and Anataa you can extend equanimity towards other beings. This is a complex topic. The following link provides you with a detailed explanation of four Brahama Viharas.

https://www.accesstoinsight.org/lib/authors/nyanaponika/wheel006.html

No matter what the christian puthujjanas and their secular humanists children claim, compassion is not metta nor karuna, and love is not metta. Compassion has nothing to do with a puthujjana trying to stop being a puthujjana.

THe pali word for compassion is and always will be Anukampa.

TO do something out of anukampām means, with the vocabulary of toxic philosophers, to do something while having pity, having mercy, compassion, and in terms of other words, to know that puthujjanas have a miserable life and to tell the few puthujjanas who want to hear about the cessation of dukkha. There is zero emotions involved, zero pathos involved, zero suffering involved on the side of the buddha who do something out of Anukampa and teach for the sake of puthujjanas.

But of course, puthujjanas are stuck in their toxic craving for kama and they try to define ''being a good person'' has having certain emotions and ''being a bad person'' has having certain other emotions. Toxic puthujjanas are stuck on the level of pathos and the toxic people like the humanists claim that having the pathos of feeling sad when they see puthujjanas not enjoying themselves is a good thing. THose people have been around for many generations now and they still have not alleviate the suffering of anybody. But they still claim that their view is correct.

The puthujjanas before the toxic humanists where here typically said that a ''good person'' can sleep peacefully, precisely because of a lack of regrets, because such a person has done nothing which is shameful [typically there a virtuous actions, and morality is disconnected from intentions]. But for the humanist puthujjana addicted to sensuality, that is not possible, precisely because, according to their toxic view, ''a good person'' sees how miserable other puthujjanas are, to the point that a good person cannot sleep at night. The view stems as usual in taking the opposite side of the view create before: with those puthujjanas is is all about intentions and actions do not matter much. As long as the humanists delude themselves into thinking that they have good intentions, no matter what they do, they will think that they are good people.

But it gets worse for those toxic people: they claim that what is left when they are humanist is their moronic fantasy of unconditional love, of accepting everybody and as usual, their favorite words ''being compassionate''. This stems from their awful dichotomy of opposing hate and love and their idiotic fantasy of ''enduring the suffering of other people'' like their jesus and bodhisattvas.

But it gets even worse: once they hear that the dhamma is about destroying hate, anger and so on, since those toxic puthujjanas addicted to emotions cannot stop thinking they are already good people for feeling sad when other puthujjanas cannot get the objects of their sensual lust, they pass the lack of hate and ignorance as their compassion which leads them to never ever manage to have right intentions. Those people completely fail to distinguish between ''kamma that is bright with bright result'' and the ''kamma that is neither dark nor bright with neither dark nor bright result'', by clinging to their moronic dichotomy of hedonism-selflessness and their toxic view that delight in the 5 strings of sensuality is not harmless as long as they feel compassionate.

If you want to train for metta, you calm the body, the mano typically by following the breath for 1h, then you focus on a living being you like, like a pet, and how much you want them to stop ''suffering'', which for a puthujjana means ''enjoying the things they like and avoiding the things they dont like''. Quickly a pleasant emotion will arise, like the sukha and piti but more calm, and perhaps even the famous cessation of subject-object, the cessation of ''a doer'' will happen. THis state is the famous state that puthujjanas who have zero wisdom, like the hedonists who invented the Mahayana and vajrayana, pass as nibanna.

When you have this good emotion for any human who focus on, you can claim to have metta. Once you have metta, or at least have this good emotion for the people you love, you can focus on doing karuna and having mudita. Since puthujjanas know nothing about the dhamma, they cannot teach it and non-puthujjanas who are not arhant have better things to do than teaching the doctrine. The day you manage to become an arhant, you can start focusing on Anukampa as the teaching of the dhamma. In the meantime, if you want to do karuna, you can support the contemplative and the other people.