iPhone update failed now stuck in Recovery Mode
This is a tough one as once you are in recovery mode you can't backup your phone. So tell us, were you backing up to iCloud or had you been backing up to a Mac or PC using iTunes? If not you may be out of luck.

What you need to do is get it out of Recovery Mode. I can't locate the info for the older SE model but you could try these.

On iPhone 8, 7, 6, 6s, 5 and earlier, hold down Power Button to turn off your device.
On iPhone XS, XS, XR, X, press and hold the side button with either volume button.

Once the phone has powered down, power it back on normally and hope it comes up out of recovery mode.

If that happens you should back up the phone with iTunes immediately then go to

Settings > General > Reset > Erase all content and settings.

Once that is done you should be able to update your phone and then restore from the backup you just made.

If it didn't come out of Recovery Mode You may need to enlist professional help. I have also seen a lot of utilities out there that can supposedly either backup an iPhone in recovery mode or get it out of Recovery Mode. I have no experience with these utilities, I have no idea if they do the job they say they do or are just backdoors to some kind of malware. So find an iPhone expert (Apple store or otherwise) who can fix this issue.

And for heaven's sake start backing up your phone on a regular basis. Either to a computer or to iCloud.