Selfhosted

First thing, back up your data in case something goes south.

With that out of the way, I have done this exact thing many times with both zfs and an array managed by mdadm. Depending on the filesystem on top of your raid array, there may be some additional commands you'll need to run to extend your partition to use all of the available space in your larger array. You do have to wait between each disk swap to wait for the array to rebuild so it might be quicker to just make a backup, remove the old drives, and build a new array with your new drives and then copy the data back over. That being said, it is fun to hot swap all of those disks and not lose any data or have downtime assuming everything goes smoothly.

Yes, it's a bad idea to do it this way. The most likely time a RAID array will fail is during a rebuild as that is a whole bunch of drive activity over a sustained timeframe.

Better to perform a backup or copy, power down, remove all the old drives, install the new ones, power back up, configure a new array (most people recommend to use RAID 6 at a minimum, no hot spare, so you have two drive redundancy) then restore or copy back the data.

This way you can also keep the old drives as a cold backup of sorts, potentially reimporting the configuration if needed.

You might also want to check that your controller really supports hot-swapping. Not all do.

Do you really need the RAID online all the time? Because if you can afford to shut it down for a few hours, it is way less work to do a backup, and then build a new RAID with your SSDs.

I'm not sure if the RAID controller will like two different kind of drives. I'd check the docs if it says something.

Consider moving to RAID-6. Single redundancy is not cool anymore.

The answer to this is going to depend on your raid controller. Frequently the answer is yes, but some raid controllers are more particular about exactly what drives are in the array. Software raid controllers are typically more forgiving of this type of change.

The "Right answer" is copy all the content to another device, upgrade disks, copy content back to new array that can take advantage of the larger disks. Or even safer, set up a completely new device in parallel and then copy data over, decommission the old device.

Some RAID systems will let you do what you say, but will not let you expand the usable storage space. Some will have particular disks they'll even take. It really depends on the RAID system.

I have a feeling you'd end up with a bunch of big drives with small volumes on them if it did work.

Warning you, I've had issues with RAID combining SSD and HDD. Basically I was on an older dell server and I wanted to do mirroring and the bios straight up refused to do it because it didn't want to mix ssds and hdds.

You've got the right community IMHO. This is something that I've never tackled but I could imagine that it would work. Just make certain you have solid backups just in case the worst should happen.