Shadow Delegation

Delegating your NFT is handled via delegate.xyz (opens in a new tab). For shadows to work via delegate.xyz (opens in a new tab) you need to click the "Shadows NFT" option to trigger your shadow NFT's movement as well as "all chains" or "Apechain".

Shadow NFT Delegation on delegate.xyz

If you just perform a regular delegation on delegate.xyz, then this wouldn't have any effect on shadow ownership.
If you do not issue a shadow delegation, your shadow (soulbound) will exist in the same wallet as the underlying asset.
If you do issue a shadow delegation, the shadow will move to that delegated wallet.
If you have multiple shadow delegations, asset ownership is determined by specificity first (token delegation overrides contract delegation overrides wallet delegation), and ties are broken by recency (newest wins).