You are dealing with two different things here, the business maybe UK tax resident but as you’ve said some of the directors aren’t. You’d have to check specifically with Monzo whether all directors have to be UK tax residents and residents as well as the business, I’d suspect they do.
Tax residency generally (and this can vary from country to country) means that you spend more than 183 days in a country, your centre of interests (so primary home, job, generally life, is in that country. If I move from Germany to the UK, for the first 182 days I am in the UK I could still be German tax resident. On the 183rd day I become uk tax resident, even though I have already been UK resident for 6 months. For that first year I may still have to file a tax return and pay taxes in Germany even though I am living in the UK. This is a very basic explanation and is too simplistic really but residency and tax residency are two very different things.
Covid has caused much confusion with this recently as people have found themselves in a different country to the one they live and pay taxes, be it because they got stuck at a second home, were abroad for work, were travelling, or whatever, borders closed and they were unable to return home at the intended time and could find that they end up becoming tax resident in a different country, at least for a year, and have to file a tax return in that country.