When can favouritism be officially not ok?

[Workplacebias]

Boss just took a big promotion. Currently In handover period. Their role successor yet to be confirmed.

Boss going all out to promote a junior staff member into a higher role before changes kick in. IMO very noticeably and unfairly so. Backstory boss had promised person this before their role change announced but not entirely in their remit to decide. Boss and the junior are very good friends outside of work. Boss has no time to spend with more senior staff/ talk to me about other issues but all conversations come back to promoting their “friend”.

Tips on how to handle?

I'm not sure there's a lot you can do really. Is the junior person worthy of promotion? Will they become your new boss?

If you want more time to speak to your boss about pressing issues - address that.
What has the Junior got to do with you - are you losing out on a promotion? I don't understand why this situation is your concern?

From a legal perspective, there isn't any indication from your description that your employer has discriminated against other members of staff, eg giving preferential treatment to the junior colleague compared to other employees based on a protected characteristic.

An example of where this type of promotion can be unlawful, is if another suitably qualified colleague were to apply for the same promotion opportunity and were for example of childbearing age, or perhaps with school aged children who the manager didn't want to give the promotion to because they have childcare responsibilities or "might go off and have babies", then it would be for the person affected to raise concerns or a grievance.

It is difficult to see how you are directly impacted other than being resentful of them receiving a promotion.

What's stopping you from setting up a regular 1:1 meeting to discuss priorities that fall into your area of accountability?