Hmm, I transitioned from Gmail to my own domain years ago, but it's still Gmail. However, I'm still both receiving and sending mail from my old @gmail.com address, using POP. Do you know if that's still possible?
I also have an old Gmail account that I don't use directly anymore. Instead of POP, I set it up to forward everything to my mailbox.org account. It works for me this way for several years now. The only issue is that I don't get the spam forwarded, so you can't see if there are false positives. You can still see it in Gmail if you occasionally log in. For me, since this is a rarely used account, the spam I get is usually indeed spam, so I don't miss it. It might be different for a more active account, though.
For sending in Mailbox.org webmail there is a thing called alternative senders where I can add email addresses to send from. I have something similar on my Android K9 app, where it's under Manage identities where I can also add the allowed senders.
I set it up a long time ago this way and I'm unsure of I had to somehow configure Gmail to be able to send from my other account. But I have the same also for @live.com and @zoho.com as I was trying different providers. This allows me to easily reply to forwarded emails with the old email addresses.