SIGHASH_ANYPREVOUT has been designed as I understand primarily for the eltoo channel construction use case although it has many other potential use cases too.

It was stated on Twitter that the proposed opcode CHECKTEMPLATEVERIFY can also support eltoo channel constructions. Is this the case?

The second part of that tweet ("APO isn’t enough on its own for Eltoo") I think is just false unless they are referring to ANYPREVOUTANYSCRIPT.

Jeremy Rubin stated on IRC that CTV commits to all scriptsigs and sequences whereas ANYPREVOUT does not.

He also stated that CTV and CHECKSIGFROMSTACK can emulate ANYPREVOUT but I haven't found further details other than what it is in the BIP.

BIP 119 states:

Were both OP_CHECKTEMPLATEVERIFY and OP_CHECKSIGFROMSTACKVERIFY to be added to Bitcoin, it would be possible to implement a variant of Eltoo's floating transactions using the following script:

witness(S+n): <sig> <H(tx with nLockTime S+n paying to program(S+n))>
    program(S): OP_CHECKTEMPLATEVERIFY <musig_key(pk_update_a, pk_update_b)> OP_CHECKSIGFROMSTACKVERIFY <S+1> OP_CHECKLOCKTIMEVERIFY