If using IMAP, all local actions are passed from the local client to the IMAP mail server - and thereafter to other logged-in mail clients.
If the IMAP server doesn’t support different flag categories (i.e., flag “colours” as now implemented within iOS/iPadOS 13.x), then the functional nature of IMAP is such that your local email client will subsequently re-sync its “local” view of the server at the next synchronisation cycle. Said another way, the server has the “master” version of your email messages - each client only has a “copy” that is effectively locally reset on each sync-cycle.
Different email providers offer different features within their IMAP server implementation - for example, Google would be considered very feature-rich, whilst your (and my) experience of Yahoo’s implementation would suggest something close to the other end of the scale; Apple IMAP implementation would be somewhere in-between these two extremes. Google and Apple support different flag colours - Yahoo and derivates don’t have this support.
As such, I don’t believe that you are seeing a fault - but instead a difference in IMAP implementation between email service providers.
As for your other issues, if still using iPadOS 13.1.x, you would be well advised to update to the current version - which at time of writing is iOS/iPadOS 13.3.1.
