The best advice I can give you is to use bigserial for B-tree friendly primary keys and consider a string-encoded UUID as one of your external record locator options. Consider other simple options like PNR-style (airline booking) locators first, especially if nontechnical users will quote them. It may even be OK if they’re reused every few years. Do not mix PK types within the schema for a service or application, especially a line-of-business application. Use UUIDv7 only as an identifier for data that is inherently timecoded, otherwise it leaks information (even if timeshifted). Do not use hashids - they have no cryptographic qualities and are less friendly to everyday humans than the integers they represent; you may as well just use the sequence ID. As for the encoding, do not use base64 or other hyphenated alphabets, nor any identifier scheme that can produce a leading ‘0’ (zero) or ‘+’ (plus) when encoded (for the day your stuff is pasted via Excel).
Generally, the principles of separation of concerns and mechanical sympathy should be top of mind when designing a lasting and purposeful database schema.
Finally, since folks often say “I like stripe’s typed random IDs” in these kind of threads: Stripe are lying when they say their IDs are random. They have some random parts but when analyzed in sets, a large chunk of the binary layout is clearly metadata, including embedded timestamps, shard and reference keys, and versioning, in varying combinations depending on the service. I estimate they typically have 48-64 bits of randomness. That’s still plenty for most systems; you can do the same. Personally I am very fond of base58-encoded AES-encrypted bigserial+HMAC locators with a leading type prefix and a trailing metadata digit, and you can in a pinch even do this inside the database with plv8.