Improve login flow and fix "Open with browser" UX issue - update ecosystem.json file again

[tapbase]

What changed? Why?

This PR addresses two issues:
Desktop login/connect issue: Users accessing the app from desktop (e.g., from base.org) can now log in and connect without problems.
"Open with browser" confusion: The button no longer leads to a deadend for users who aren't logged in. It's been updated to avoid misleading behavior and improve clarity.

Notes to reviewers

How has it been tested?

Have you tested the following pages?

BaseWeb

• [] base.org
• [] base.org/names
• [] base.org/builders
• [] base.org/ecosystem
• [] base.org/name/jesse
• [] base.org/manage-names
• [] base.org/resources

BaseDocs

• [] docs.base.org
• [] docs sub-pages

[vercel]

@tapbase is attempting to deploy a commit to the Coinbase Team on Vercel.

A member of the Team first needs to authorize it.

[cb-heimdall]

🟡 Heimdall Review Status

Requirement	Status	More Info
Reviews	🟡 0/1	Denominator calculation Show calculation 1 if user is bot 0 1 if user is external 0 From .codeflow.yml 1 Additional review requirements Show calculation Max 0 0 From CODEOWNERS 0 Global minimum 0 Max 1 1 1 if commit is unverified 0 Sum 1

[wbnns]

@tapbase Hello, please see the readme for steps on Ecosystem additions, this PR does not conform to the requested format. 🙏