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Icon packs are coming [1] and you can set your own for the more niche sites.

The problem with querying websites for their icon is that it leaks data about you (your phone and desktop) to a third-party without a proxy, requires a domain to match against, and like with Authy, the icons go out of date and become inconsistent. Worst of all, you have to give network access to the entire app for a trivial feature, making it less secure and trustworthy. Offline icon packs that have a consistent look is a good solution to all of this. [2]

[1] https://github.com/beemdevelopment/Aegis/issues/509

[2] https://github.com/aegis-icons/aegis-icons

Bitwarden has this feature, and it is optional. I wouldn't mind if Aegis has it, as long as it is optional.

Authy now adds the site logo automatically. If not, you can search one up in the app