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From: Jonas Nick <jonasdnick@gmail.com>
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To: Michael Folkson <michaelfolkson@protonmail.com>,
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Subject: Re: [bitcoin-dev] BIP draft: Half-Aggregation of BIP-340 Signatures
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To be clear, whether "half aggregation needs a new output type or not" does not
become clear in the draft BIP because it is out of scope. Half-aggregation has a
few possible applications. The draft only specifies the cryptographic scheme.

The StackExchange post you link to argues that CISA requires a new output type.
The same argument applies to half aggregating signatures across transaction
inputs (CISHA, if you will). The only difference to "full aggregation" is that
the transaction signature is a single half-aggregate signature instead of a
64-byte signature. You're right that it's possible to do batch verification of
Taproot output key spends (Schnorr signatures) and script spends (key tweaks).