Traveling by train from Spiez to Paris - is a 32 minute layover long enough?

Plenty of time! 10 minutes would be easy as well.
Looking at www.sbb.ch/en, you arrive on Track 11 and depart on Track 6. You just get off your arriving train, walk to the escalator up to the cross over bridge, walk about 100 ft to the escalator down to Track 6 and wait for your train to Paris. Should take you 5 minutes all told.

Since your ICE train from Spiez is continuing on to Berlin, be prepared before you arrive at Basel. Have all your luggage gathered together and be making your way to the train door so you can exit as soon as the train stops.

For train travel that is a life time. You can have lunch, send text messages home, use the water closet, and maybe take nap.

as the others have said, that's an age.

You might try to see where the escalators are relative to whichever car number you will need to get to for your Paris train so you know which way to turn when you reach the train.

You won't find many pretzels in Paris so you will likely have plenty of time to load up at one of the Bretel König stands in Basel SBB. Good snacks on offer throughout the station. Coffee too.

You do need to be on the Lyria TGV to Paris a minute or two before departure so don't dawdle too much...

Its not like making an airline connection, where there is check-in and baggage handling etc. Its like the subway or city bus transfers where it only takes a few minutes to walk to the track where your next train will be. If it's there get on. If not there yet, wait until it shows up. Just make sure its the right one, as there is no gate agent to make sure you're getting on the right train.

Stan makes a good point. With that much time you could find another train on your track ready to leave so make sure it is your train. Generally there will be someone with a uniform somewhere. And don't hesitate to ask another passenger if this is the train to ????

There will also be indicating boards on the platform telling what the next train on the track will be. Also, just keep in mind that the TGV Lyia train should arrive at 12:30 from Zurich, so if a train comes by at 12:10, that is not it. Plus, it will look like this:
https://en.wikipedia.org/wiki/TGV_Lyria#/media/File:Paris-Gare_de_Lyon_DSC_1395_(49651815078).jpg
Note the double decker configuration.

It used to be that the change in Basel was only 4 minutes, cross platform and a perfect example of how train travel should be.
But SBB needed to add a few minutes on the IC services to Basel because of works on the route, and SNCF could not be convinced to change their TGV schedule. So now we have this annoying long change inflicted upon us.
I hope that once the works in Liestal are over the schedule goes back to how it was, and I can get from Interlaken to Paris half an hour quicker.

We remember those four minute changes. Did lots of them, but, they were doable. 32-minutes is a big moment in time in terms of train connections through Basel.

We just had a 3 minute train change last week getting on the last segment to Rothenburg- had 2minutes to spare! You could easily tell the passengers who hadn't done this before- they're frantically waiving to the train engineer to please wait, as they drag luggage down the stairs, and then back up again. The trains weren't on adjoining platforms.
PS - This is why RS advocates carry-on sized luggage.

I really like riding on the German ICE trains, and your 10:22 departure from Spiez is the ICE from Interlaken to Berlin. It will be comfortable and ever so quiet. It only leaves Interlaken 20 minutes before you join it so it is very unlikely to be late.

But if you want to you should be able (don't know if your precise ticket requires you to travel on that 10:22, if just the Paris train is reserved you can travel to Basel by an alternative) to take the half hour (28 minutes) earlier train from Spiez to Basel. It will be an EC (EC50 if my memory is right) from Milan. Then you would have a whole hour in Basel to take in the sights of the station, especially the mural over the booking hall....