D&D Beyond does not support structured search for traits
There is, due to copyright, no other easily searchable, legal source for all the published monsters in 5e. The only site that legally can provide all of them is D&D Beyond, and the search function there does not currently allow you to search full text on traits, which is where legendary resistance is recorded.
However, at least checking the Monster Manual, all the creatures that have Legendary Resistance also have Legendary Actions and therefore are Legendary themselves. Nearly all in Volo's Guide to Monsters, Mordenkainen's Tome of Foes, and Monsters of the Multiverse are too.
Your suspicion is right, though, not all monsters with legendary resistance are legendary. Notable exception are
Name |
CR |
Source |
Aerisi Kalinoth |
7 |
Princes of the Apocalype |
Aphemia |
5 |
Mystic Odyssey of Theros |
Dragonborn of Bahamut |
8 |
Fizban's Treasury of Dragons |
Dragonborn of Sardior |
6 |
Fizban's Treasury of Dragons |
Dragonborn of Tiamat |
7 |
Fizban's Treasury of Dragons |
Ebondeath |
4 |
Divine Contention |
Galvan |
7 |
Rise of Tiamat |
Gar Shatterkeel |
9 |
Princes of the Apocalypse |
Ghost Dragon |
7 |
Fizban's Treasury of Dragons |
Harshnag |
9 |
Storm King's Thunder |
King of Feathers |
8 |
Tomb of Annihilation |
Marlos Urnrayle |
8 |
Princes of the Apocalypse |
Marut |
25 |
Monsters of the Multiverse |
Necrichor |
7 |
Van Richtens Guide to Ravenloft |
Runara |
13 |
Dragons of Stormwreck Isle |
Vanifer |
9 |
Princes of the Apocalypse |
Warforged Colossus |
25 |
Eberron: Rising from the Last War |
Zodar |
16 |
Boo's Astral Menagerie |
Some like the Marut or Apemia still show up on D&D Beyond as Legendary, but the others don't.
I am not sure if there is a very systematic way the "Legendary = Yes" rider is applied on D&D Beyond in these ambiguous cases, but your search for legendary monsters should work reasonably well.