Linux

I have had the exact same issue as you. Thunderbird is great, but their attachment search is not. I spent a lot of time looking for a way to make it work and what I settled on is using a third party program to serve this function: Recoll (https://www.recoll.org/index.html).

It should be available in your distro's package repository.

You'll need to download your messages to your computer, but it will work in the way that you expect search to work (I.e. search by filename, search by text within attachments, search by text within emails). Setup is straightforward. You just need to point it to the Thunderbird profile directory where your emails are saved. As a bonus, you get good desktop search for all the other files on your computer too.

Sadly (don't throw anything at me), the only desktop email program that I have found that does search properly is Outlook desktop. On Linux, that is obviously a non-starter.

I use evolution and it works well for everything besides my work Gmail but that has more to do with security policies than evolution

mutt or nothing

Where indexing and searching mails is concerned, notmuch is the best I've seen. Do note that this is not an e-mail client, it only indexes, tags and searches (following the "UNIX philosophy" of doing one job well).

I personally use it with neomutt as a mail user agent, which is almost certainly not what you want. Notmuch supports other clients but they're all pretty arcane.

So this is not a recommendation, just a glimpse into advanced e-mail setups I guess.

I've always liked Thunderbird. Geary is also nice. Not sure if it can attachment search.

You can filter messages with attachment on Thunderbird btw

maybe evolution is what you’re searching for

Geary or Mailspring are the best options. Neither is perfect. I lean toward Geary.

Tired of Gmail? Switch to Kmail!

Claws Mail https://www.claws-mail.org/

Claws searches reasonably quickly and unlike thunderbird it isn't a total resource hog. OTOH it suffers from not being multi threaded, which means when you first install it, expect it to take literally hours before it finishes syncing all your emails.

Mutt is not multi threaded either. Only thunderbird and kmail are, and kmail is a buggy mess, while thunderbird eats your ram like it's a plate of cheese danishes.

nmh is the way

Why not Roundcube ?

I use Betterbird as my main email client so I tried out the attachment searching. Searching by attachment name seemed to work well, but it doesn't look like it searches for the text within the documents, at least not for PDFs. Not sure if there's like an OCR extension or anything that would do it, but yeah just the base Betterbird install doesn't do it as far as I can see.

You may find what you need here or there.

Like @a14o@feddit.org I would personaly recommend the power of neomutt and notmuch, but it's not a GUI option if that's what you're looking for.