Nationwide - this is down to Nationwide. They (and other banks) are obliged to make so-called payment accounts available via API (e.g. current accounts and credit card accounts) but whether or not they make other accounts available is up to them.
PayPal - Possibly the same issue.
HL in Moneyhub - This is likely just HL active savings and not HL investment accounts. Unclear if Emma is planning to connect - (Most-Wanted 🇬🇧) integrations - #1151 by edoardomoreni
Freetrade - doesn’t have an API