How to transfer a pdf to apple wallet ?

Wallet only contains cryptologically secured “digital mobile credentials.” It’s not a repository (folder) for simple scans.

Any additions to Wallet will need to be accomplished electronically by the agency who issued - or otherwise tracks - the original vax(s).

Not all agencies do this.

If all you desire is a convenient image of your Vax card(s); adding to Notes is a viable and easy-to-use solution.