[OT] Question about rules around appointments

I see that Trump is hoping to appoint at least two members of the House to posts in his government: Elise Stefanik as UN Ambassador and Matt Gaetz as Attorney-General. I know that Gaetz has already resigned his seat but haven't heard if Stefanik has too.
Do House members have to resign their seats before they qualify for senior jobs like this? It seems odd to me that they would give up their seats prior to actually getting confirmed in the job. After all, Republican control of the House is very narrow. I'm assuming that special elections will be held to replace Stefanik and Gaetz and there seems like at least SOME risk that those seats could be lost to the Democrats, meaning that control of the House could be lost to the Democrats if enough of the not-fully-counted seats go their way.
It would make more sense to me to nominate Gaetz and Stefanik but leave them in the House until their appointments are approved; if they are NOT approved, they'd still have their seats in the House rather than potentially losing them to the Dems.
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Rhino