[PM-4781] Update badges and add Bitwarden icon to README

[meenbeese]

Type of change

• Bug fix
• New feature development
• Tech debt (refactoring, code cleanup, dependency upgrades, etc)
• Build/deploy pipeline (DevOps)
• Other

Objective

I did a minor facelift by updating the README with newer badges and adding our mobile icon.

Code changes

• README.md: Updated with new badges (old ones are outdated/blurry), and they are local so there is no need to fetch data from Imgur every time. Also, added our app icon because we have it on Desktop clients so it makes for mobile clients as well. New readme should look better and load faster as a result of these changes.

Screenshots

Before
After

Before you submit

• Please check for formatting errors (dotnet format --verify-no-changes) (required)
• Please add unit tests where it makes sense to do so (encouraged but not required)
• If this change requires a documentation update - notify the documentation team
• If this change has particular deployment requirements - notify the DevOps team

[CLAassistant]

All committers have signed the CLA.

[bitwarden-bot]

Thank you for your contribution! We've added this to our internal Community PR board for review.
ID: PM-4781