There is a new option now:
Proton wallet.
Oh wow, from a reputable company.
But it appears it's not fully open to public yet so they just enter me to waitlist when I logged in. We could skip this in two ways apparently.
Invites from active users of Proton Wallet will allow you to skip this waiting list.
You can also support us and get immediate access by upgrading to Proton Visionary, our most premium plan with paid features in all Proton products.
By active users, IDK if they meant active users on their platform regardless of account tier or just active in some subscriptions like what they tell here:
Proton Visionary and Lifetime users have limited invites to share with anybody they want.
Invited users will also receive a smaller number of invites, as the ability to invite some friends makes Proton Wallet more useful.
I haven't extensively checked the wallet, but I am seeing a sign-up window to create a proton account. With all this, do they still offer an option for one to back up their and later import wallet seeds, making it a self-custodial web wallet?
Apparently, yes!
Each wallet has a recovery seed phrase that’s only known to you (Proton never sees it). Even if Proton were to entirely disappear someday, you would still have access to the Bitcoin in your Proton wallet with your recovery phrase.