I'll preface this by saying that this may be a question that would be better asked on a forum of like-minded animal owners, some of whom will have tackled similar builds and they'll be able to report what worked and what didn't.
It is very difficult to seal wood off completely from moisture using common coatings and finishes. Most of the time when woodworkers say "seal the wood" they're speaking informally...... very informally, because most coatings only do a partial job of isolating the wood from its environment and some do almost nothing!
Products that will 100% waterproof wood include bartop finishes, marine epoxy coatings and fibreglass resin, but in addition to their waterproof nature for a complete seal it also requires them to be put on thickly, the equivalent of perhaps 20 coats of regular varnish, so there is a very significant coating on the surface.
The good news is I don't think you need to go that far. Because many similar habitats I've seen, built mostly from plywood, seem to be finished off in basic coatings (probably varnish, based on the appearance and guesswork) and not in something visibly thick and with a slick, high-gloss finish.
My suspicion is that if you use a decently water-resistant material (e.g. a suitable grade of plywood and/or any solid wood that naturally does well outdoors) and simply varnished it thoroughly that you'd get the performance you want. For this I'd use polyurethane* which has good scratch-resistance. Apply four full-strength coats minimum, but six or seven would be better. If you wipe the varnish on to make it easier to apply (see wiping varnish) you'll want to use at least 7-9 coats for an equivalent to four unthinned coats applied by brush.
*I mean oil-based poly here and not the waterbased type which is a completely different thing.