Witches not spawned by raids (spawn eggs or natural spawning) can only participate in raids once. Naturally spawned witches can participate in raids multiple times if the witch's RaidId tag is removed or changed to 0.

Steps to Reproduce:

1. Spawn a witch within 96 blocks of the village center.
2. Begin a raid in that village.
3. Cause a "Raid - Defeat".
4. Begin another raid.

Observed Results:

The naturally spawned witches don't become part of subsequent raids.

Expected Results:

Naturally spawned witches join subsequent raids.

Screenshots/Videos:

Minecraft 1.17.1 - Singleplayer 2021-10-07 15-18-12_Trim.mp4

Notes:

Grounds for this being a bug:

"In Java Edition, illagers and witches not spawned as part of the raid (e.g. from a patrol) may join the raid and be counted by the bossbar, provided they are within 96 blocks of the village center."

-Minecraft Wiki (link to specific page and section: https://minecraft.wiki/w/Raid#Joining)