iPad Pro 1st gen so slow it's unusable

Have you tried a forced-restart - as this will release resources, improving performance:

Force restart iPad (models with Face ID or with Touch ID in the top button)

If your iPad doesn’t have the Home button, do the following:

1. Press and quickly release the volume button nearest to the top button.
2. Press and quickly release the volume button farthest from the top button.
3. Press and hold the top button.
4. When the Apple logo appears, release the top button.

Force restart iPad (models with the Home button)

Press and hold the top button and the Home button at the same time. When the Apple logo appears, release both buttons.

Ensure that you have updated your iPad to the most recent version of iPadOS - at time of writing, this being iPadOS 16.5.1.

If your iPad is capable of update to a more recent version of iOS/iPadOS than is currently installed, these support pages outline both the available methods by which the update can be performed - and troubleshooting should you experience difficulties:

Update your iPhone, iPad or iPod touch – Apple Support

If you can't update or restore your iPhone, iPad or iPod touch – Apple Support

If your iPhone, iPad or iPod touch won’t update - Apple Support

iOS update and restore errors – Apple Support

How much free internal data storage space is left on your 2015/2016, 1st gen iPad Pro?

I have the same model iPad Pro as you and I have a 256 GBs storage model with, approximately, 28 GBs left.

My 2015/2016iPad Pro is working just fine.

Your iPad needs, at the very least, between 6-8 GBs free internal data storage space, to operate at an acceptable/nominal level.

Forced restart seemed to really help. Not sure why I didn't try it first! Thank you

You're very welcome. I'm delighted that the problem was easily resolved.