Funnily enough, I found Messenger to be the worst of all their offerings. The lack of searchable history, the terrible (terrible) scroll-back, the default always-on-screen notification bubble, the way they forced the standalone app down users' throats by disabling messages in both the FB app and the mobile web version, all really turned me off to it.
Use https://m.me - It's the web app just for Messenger; on my desktop I launch it via Chrome with the --app= param so it runs in it's own window.
Click on the ⓘ that's located in the top right of a conversation, and you'll see the search option (among other things).
I've long since abandoned Facebook, but I wouldn't be surprised if a similar IFTTT feature exists to export tagged photos into Google Photos. If I recall this only works for 'new' photos posted that you are tagged in, it doesn't appear to pull images from before you enabled the IFTTT service. At any rate, this lets you see photos you are tagged in without ever having to actually use your Facebook account.