Large GMail mailbox - close to 800,000 unread emails - best email client to use?

I have a rather large Gmail mailbox with close to 800,000 unread emails the the last 13 years and never got much done because I have to search for emails by email address and ofcourse the browser(s) will lag after a few pages where there are 100 emails displayed per page and inefficient. What is the best free clients for handling a large email mailbox and can sort by sender name or email domain first and after that, sort by chronological order based on those results. And for the clients, when I move the message or delete, does it basically put the deleted messages in the trash and move messages to a different folder, will it also be in the trash and folders on the web interface afterwards? Thanks!

Even though I have Outlook from MS office, I tend to advise people to use Thunderbird.
It's free, highly customizable. Their new SuperNova interface is very good.
Keep in mind that because your mail box is IMAP, in order for sorting to happen, downloads locally must happen, at least for headers.
This, regardless of the client, might take some time.

Many thanks @OAT and I should have said Free clients in the original post which I have updated now. I tried using Thunderbird and other non-Microsoft free clients many years ago, prior to 2019, probably before even 2017 and I forgot what was wrong when using it but I am sure I was using IMAP and not POP3 but what was deleted and no longer in the inbox on the client was still showing up in the inbox and not the trash when using gmail on the browser which was why I gave up back then without looking at it again. I'll give Thunderbird a try and then ask for help with the sorting if I can't figure it out.

Give eM Client a try, it has a free version for up-to two email accounts and is better than Outlook IMO.