For Rarity and Stats, go to the DMF. Take a look at the DMF tamers. They DO obey the rarity rules - Jeremy Feasel's pets have 10% higher stats then the rare versions you field against him. Christoph VonFeasel has 20% more then the rare versions you can field against him.
Now compare Christoph's pets to ANY SL tamer. Notice how every single SL tamer rare pet has 2-3k more HP then Jeremy's Cow (H/P Breed), and roughly 400-600 more stats split between speed or power then Christoph's pets? That's power creep in the absolute grossest form possible. A single pet from any of the SL tamers is almost as tough as a lvl 25 Cata tamer's entire TEAM. That is outright bad and sloppy design, when instead of trying to come up with new or interesting fights (BfA had a handful of interestingly designed pet fights, SL has only one), instead just make everything 2x as strong.
Do you mean Tanaan or Nazjatar/Mechagon? I stated that Tanaan was fine in terms of balance. Nazjatar/Mechagon is not. SL is even worse. When you looked at Nazjatar pet battle strats, while you may see various strats around, they essentially revolved around just a handful of different movesets.
1: Unborn Val'kyr (Almost every boss pet battle strat has at least one, because of Doom + UA)
2: Black Claw + Stampede variants.
3: EXPLOSIONS followed up by Heavy Hitter
4: My all-time favorite, 3x Heavy Hitters (Hey, if 3x Chrominimus won't finish it off, nothing will)
The only times you had variations outside of that was to deal with specific pets, like the Mechagon one that was immune for 3 out of every 4 turns, or the Kelp one that healed itself back to full health every 3rd turn.
Finally, by type matching, I don't just mean "Mechanic pet vs Beast". I mean more along the lines of "Flying pet with Mechanic moves to go up against Beasts". And back in the day that worked, and I was able to acquire a full set of counters like that, which excelled at pretty much all pet content without having to go up against Howlbomb (Nerfed initially in MoP with the Pandaren Water Elemental, removed in WoD).
When Blizzard nerfed most of the popular strats to get through Nazjatar/Mechagon pet battles, I was hoping that they would also tone the strength of SL pet battles on down. But nope, if anything they doubled down on it.
Glurp - Will one-shot any active pet every 3rd turn.
Sewer Creeper - Will alternatively one-shot your pets.
Veilwing - Will also one-shot your pets if you don't change the weather.
Kostos - Extremely frustrating fight that requires specific movesets to beat both the shield, the heal, AND the one-shot.
Countess is the only "normal" pet boss battle out of SL pet battle content so far, in which as long as you brought either resistant pets or pets with magic damage you would be able to win. Gelatinous/Digaro is essentially trivialized by Shell Shield - Digaro will murder your entire team if you lack it, but deals no damage if you have it. Gelatinous will murder your backline pets, but can't kill anything with Shell Shield or equivalent. Briarfang needs his single damage move dodged, and the fight will take a bit since he immunes every 3rd round. Chittermaw needs extremely heavy hitters, and Crystalfang needs Darkness+Burst to be downed.
And there is undeniable power creep expansion after expansion, along with Blizzard nerfing all the top movesets each expansion. Either Blizzard needs to come down on the power of current pet battles, or they need to quit nerfing top movesets and instead work on making interesting pet battles rather then blatantly OP pet battles.