The fact that an entity is falling off a climbable block is lost upon reload, preventing the death message for falling off climbable blocks from appearing

If a player or tamed mob falls off a climbable block, a special death message is displayed, such as "<entity> fell off a ladder" or "fell off some vines," or "<entity> fell while climbing" for non-climbable blocks in vanilla. However, the information that the entity is falling off the climbable block is not saved upon relog, so relogging while the entity is falling prevents the special death message from appearing. Relates to MC-271979, MC-270540 MC-59626, MC-69821, MC-234389, MC-257420, MC-254131, MC-257419, MC-260236, MC-254135, MC-269103, MC-135195 and MC-268972.

Steps to reproduce

1. /fill ~ ~ ~1 ~ ~50 ~1 minecraft:netherite_block

2. /fill ~ ~ ~ ~ ~50 ~ minecraft:ladder

3. /fill ~-1 ~49 ~ ~-4 ~49 ~ minecraft:obsidian

4. /fill ~-1 ~50 ~1 ~-4 ~50 ~1 minecraft:obsidian

5. /setblock ~-4 ~50 ~ minecraft:sticky_piston[facing=east]

6. /setblock ~-3 ~50 ~ minecraft:slime_block

7. /fill ~-1 ~51 ~1 ~-4 ~51 ~1 minecraft:redstone_wire

8. /setblock ~ ~51 ~1 minecraft:stone_button[face=floor]

9. /tp ~-2 ~50 ~

10. Spawn a wolf on top of the obsidian and tame it
11. Make sure that the wolf is sitting to prevent it from teleporting
12. Press the button
13. Notice that it says "Wolf fell off a ladder" as expected
14. Spawn a wolf on top of the obsidian and tame it
15. Make sure that the wolf is sitting to prevent it from teleporting
16. Press the button
17. Relog

Observed result: It says "Wolf fell from a high place".
Expectet result: It should say "Wolf fell off a ladder".