1/ Can the Senate disqualify an impeached/convicted POTUS from being elected again to the Presidency?
I think so
BUT
-It has never been decided by any court or Congress (no POTUS has been convicted by Senate).
-Some legal scholars say a convicted/DQ’d POTUS can be elected again

2/ The Constitution says the Senate can remove an impeached official and also order “disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States.” The “Office of honor...” phrase isn’t defined or used elsewhere in the Constitution.

3/ This law review article contends it would apply to a judgeship, cabinet position, and other executive branch offices, but not to a seat in Congress. (In other words, it’s argued that Senate DQ couldn’t preclude someone from being elected to Congress.) https://poseidon01.ssrn.com/delivery.php?ID=067118073027019002004088110070029099001011031068070039103005006106103087095090092086033011100024126055116029007096010090003072037001060054001025117071006104066004112072010046064102073081007079085091091096030104093031005093027031002083029125086065111067&EXT=pdf&INDEX=TRUE

4/ This law review article agrees and also suggests an impeached/removed official also can’t be barred from serving as President. https://poseidon01.ssrn.com/delivery.php?ID=348094069068099089122094120127003024022087061054024018026093006006065027028031107106002063005047108007015085101079090067126019046053082082007102076090079110007097064075087071072116123088080087108069097075099127002099070086028121091100076068004025101&EXT=pdf&INDEX=TRUE

5/ This law review article agrees no DQ for a House or Senate seat and says that the argument against the Senate being able to DQ an impeached/removed official from serving as President is “serious and detailed.” https://poseidon01.ssrn.com/delivery.php?ID=025078121121076076087097076025108009116008031085056044126101101009101073075091122065033020049102118033018089019119126070089096105041060022013113093122077098100030028018048017069100000005127083124116081094067125085102125126127102006086098019103088105&EXT=pdf&INDEX=TRUE

6/ Again, I agree think conviction and DQ by the Senate would would prevent a convicted president from being elected president again. But I’m noting the arguments against that proposition because I know you all like to get into the nuance.

7/ It’s not directly on point, but worth noting that current Rep. Alcee Hastings was previously a federal judge. Then he was impeached, convicted and removed by the Senate. The Senate did not invoke the DQ provision (it rarely has). Then Hastings was elected to Congress.