since upgrading to sequoia 15.1 my mac doesn't recognize my SSD Crucial x6 and won't print

To add to @Luis' suggestion about the "Allow accessories to connect" option in the Privacy & Security System Settings.... I have mine set for "Allow when unlocked" since it doesn't really hurt security. I did this because I was constantly getting messages to allow/reject external devices, but sometimes those pop-ups would disappear (or perhaps never appeared). I still don't understand why sometimes I'm prompted to approve/decline them and other times no notice is given, but the devices connect & activate.

As for the printers.....most printer manufacturers are terrible at driver support especially for older models that did not support AirPrint. It is up to those printer manufacturers to ensure their drivers are compatible with every OS update or upgrade. If the printer manufacturer stops providing driver updates, that is on the manufacturer, not Apple.

Before upgrading to a new major version of any OS, the user should always confirm all their hardware & software are fully compatible with the new OS. If a manufacturer is going to drop support, then that will be when they will do so. Plus it can take some third parties weeks, months, or even longer to provide updated versions of their drivers.

I did see another post on this forum where someone also had an HP printer that no longer functioned with Sequoia (official support had been dropped several years ago, but some later versions of macOS may have still allowed the older driver to work at least until Sequoia). A forum contributor discovered that the particular HP model appeared to have Air Print support.....if that is the case for you, then delete the printer & uninstall the HP driver. Reboot. Then Add the Printer, but choose the Air Print driver option.

Check both HP & Brother's websites to see if either one have updated drivers for your printer that are compatible with Sequoia.

Going forward, you definitely want to purchase a printer that has AirPrint support so an OS upgrade doesn't break the support for your printers.

There is also a possibility that if the printers are not able to be accessed, then maybe it is a networking issue (hard to say due to not having specific details of the issue & error messages involved), but something in what you wrote gave me that impression. macOS Sequoia has modified some networking aspects so you may need to turn off a few network related features....unfortunately I don't recall the name of the most likely network related feature that could be involved here.

When I connect a new drive (new in the sense that it had not been used with this mac), I get a window saying "Allow this device connect" (or some similar wording). I click Allow, and they connect.

I see that there are threads complaining about the same problem with USB drives not appearing. I wonder if, for some reason, the above window asking for permission does not appear, and then the drives are not permitted to connect - and maybe the same happens with the printer.

Concerning the printing problem, can you give more specific details about what is happening? Does the print dialog show? Does it show the name of the printer? Does Save as PDF work?

My two cents... upgraded to Sequoia 15.1 yesterday and now my MacBook Air M3 won't recognize my two printers in the office (a Brother and an HP) nor will it recognize my Brother at home (different model). Apple Support on the phone this morning could not solve either. Blamed the printer drivers ( all four????). My iPad Pro M4 works flawlessly while printing. I've tried deleting the office printers but now because 15.1 can't even see them, I am unable to get them back as an available printer on my Air. I have gotten the office HP to print from the MacBook but I have to go through the HP Smart app.