The list is exhaustive. So is the list of sub-classes, even though the basic rules / SRD doesn't detail all of them. (Other material has even more subclass options that aren't even mentioned in the player's handbook.)
Unearthed Arcana even has some new fighting-style options, including a Paladin-specific one (Blessed Warrior) that gives you two Cleric cantrips. But it doesn't give paladins existing Fighting Style options that were previously restricted to other classes.
Paladins don't get Two-Weapon Fighting.
Would it be balanced for Paladins to get TWF? Arguably no, especially at high level
Other answers suggest that it wouldn't be an issue for class balance for a DM to let a Paladin choose TWF. That's certainly not clear; Paladins do a lot of damage with Divine Smite, and one more attack per round is a big deal. Especially at 11th level for Improved Divine Smite (+1d8 radiant on every melee weapon hit, without spending a spell slot). Improved DS would make two weapon fighting much stronger than it would be for other classes, relative to other fighting styles.
(Without the fighting style, not adding a stat modifier to damage rolls with the off-hand weapon makes it probably not worth it to use two weapons instead of a higher-damage two-handed weapon, or sword+board as a defensive option.)
Also, one bonus-action attack per turn lets you dump your spell slots into Divine Smites significantly faster for much higher burst damage. From lvl 2 through 4 (without Extra Attack), you can smite twice as fast on average. At low level it doesn't take many smites to empty the tank, but a single combat often lasts very few rounds.
Extra chances to crit are also important: you're fishing for crits to get double the benefit from any spell slot you do spend. You typically save your higher-level spell slots for crits, and might not smite at all on some regular hits. Having more total crits lets you be more selective.
And more total hits lets you be more selective earlier; you know you'll be able to dump several spell slots quickly on non-crits later in the fight if you still have lots left. So there's slightly less pressure to Smite early just for total damage output. (Well-designed fights aren't single target dummies, though, so you often want to Smite early to finish off some extra enemy before it does another round of bad stuff, or whatever other fight-specific reason).
A Paladin can of course get these benefits by dipping into 1 level of Fighter (or two for Action Surge as well), so it's not game-breaking, but multi-classing has a significant opportunity cost of being behind in your Paladin levels. (And never being able to get to your level 20 capstone ability, e.g. Devotion paladin Holy Nimbus looks amazing: 10 radiant damage AoE every round for a minute in a 30 ft radius, damaging only enemies, plus other benefits, once per long rest.)
These benefits of a bonus-action attack are somewhat balanced by the action economy of casting bonus action spells. There are several Xyz Smite spells that buff your next hit with damage (and often a status effect), like Branding Smite. For pure damage output, you'd cast one of those, attack, and use another spell slot or two to Divine Smite if your attack(s) hit. That means you're limited to taking the Attack action (with Extra Attack), not also doing a bonus action off-hand attack.