Stop writing to column `user_id` of tables `profiles` and `user_filters`

This issue has been migrated from [#16181](https://github.com/matrix-org/synapse/pull/16181).

---

This is in preparation to drop the `user_id` column from these tables entirely. This was originally introduced in #15787 but was reverted in #15953 because I found some places where we were still reading from the column `user_id` of the table profiles. These reads were then dropped in #15955 which was part of `v1.89.0` so we should be able to stop writing to these columns now, and drop the column entirely next release cycle.