Self-Publishing Under a Pen Name While Trade Published Under Your Real Name

I'm sort of in that position. My first book (Outland) was completely self-pubbed. My second book (Legion) got an agent and a contract with Audible. No pen name, though. What information are you looking for?

I have not seen any indication of prejudice. Agents want a client that produces books that sell. Publishers want books that sell.

Keep in mind, though, that an offer from an agent might be for all your work until the agreement is terminated. Under those circumstances, you won't be able to continue to self-pub anything. And a publisher may offer you a multi-book deal. Same problem.

I don't think there's any prejudice. The only problem I can see is if your self published books don't sell well, and agents and publishers check on their sales to see how well your writing has done. (And yes, you'd have to be open about your pen name with your new agent.)

Note that pseudonyms are very easily broken. If someone wants to discover the real person behind a pseudonym it's not usually difficult to do that. So don't rely on this to give you anonymity. It's a useful way to separate different books, but it's not a guaranteed protection.