Is this actually established? The actual language states “The Member acting as Speaker pro tempore under this provision may exercise such authorities of the Office of Speaker as may be necessary and appropriate pending the election of a Speaker or Speaker pro tempore.”

Per this:

It comes right after the part you quoted:

The authority of a Speaker pro tempore to exercise certain powers depends on whether he is designated, designated and approved, or elected. The powers of a designated Speaker pro tempore, compared with those of an elected Speaker pro tempore, are relatively limited. Deschler Ch 6 Sec. Sec. 10, 14.

Since he hasn’t been elected or “designated and approved”, his powers are much more limited. The other important words are “pending the election of a Speaker or Speaker Pro Tempore”. This has generally been interpreted as his powers are only limited to being what’s absolutely needed to elect a permanent Speaker. As virtually everybody has said that the HoR is essentially shut down for a week until the GOP comes up with a nominee, it looks like this interpretation is still holding.

This asshole is just stroking off to the GOP base with these evictions. Hopefully, they tell him to go fuck himself.