The scoreboard objective criteria minecraft.custom:minecraft.damage_dealt_resisted does not increase when a player is hit and resists damage using the resistance effect.

However, the score does increase when a non-player entity with health points and the resistance effect is hit (tested bat, blaze, chicken, creeper, enderman, pig, snow_golem, zombie).

To replicate follow these steps:

/scoreboard objectives add dmg_dealt_res minecraft.custom:minecraft.damage_dealt_resisted

/scoreboard objectives setdisplay sidebar dmg_dealt_res

/summon zombie ~ ~ ~

/effect give @e[type=zombie] minecraft:resistance 1000 10 true

then hit the zombie, score goes up.

Have another player (host LAN, or host a vanilla server); give them resistance and hit them. score should go up but does not.

(you can give yourself resistance and shoot yourself with an arrow and the score won't go up either, but neither does the criteria minecraft.custom:minecraft.damage_dealt if you don't apply resistance: could also be a bug?)