If we advertise a loan product including a APR and a payment example do we need to include the escrow payment?

Nope but you need to disclose that the payment amount doesnt include t&i, see below for an example.

*APR is based upon a $100,000 loan with 360 monthly
principal & interest payments of $648.60 with 20% equity.
Payment amount does not include taxes and insurance, so
actual payments will be greater.

If the escrow payments includes a FC (PMI renewal premiums, for example), that portion of the escrow would have to be included in the advertised payment schedule and APR.

Can you not use the wording below?

ii. In an advertisement for credit secured by a dwelling, when any series of payments varies because of the inclusion of mortgage insurance premiums, a creditor may state the number and timing of payments, the fact that payments do not include amounts for mortgage insurance premiums, and that the actual payment obligation will be higher.