[Notebook] Browse Bar holding onto stale model, reverts changes

[jvigliotta]

Closes #7943 7943

Describe your changes:

In Browse.js instead of just watching the name of the domain object to update the page title, we watch the whole object and update the whole object, while also updating the page title if necessary.

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Author Checklist

• Changes address original issue?
• Tests included and/or updated with changes?
• Has this been smoke tested?
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• Testing instructions included in associated issue OR is this a dependency/testcase change?

Reviewer Checklist

• Changes appear to address issue?
• Reviewer has tested changes by following the provided instructions?
• Changes appear not to be breaking changes?
• Appropriate automated tests included?
• Code style and in-line documentation are appropriate?

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 57.57%. Comparing base (14b947c) to head (de4e846).
Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #7944      +/-   ##
==========================================
- Coverage   57.68%   57.57%   -0.12%     
==========================================
  Files         678      678              
  Lines       27427    27427              
  Branches     2691     2691              
==========================================
- Hits        15822    15790      -32     
- Misses      11267    11296      +29     
- Partials      338      341       +3     

Flag	Coverage Δ
e2e-ci	62.81% <100.00%> (ø)
e2e-full	41.92% <66.66%> (-0.08%)	⬇️
unit	49.35% <66.66%> (-0.15%)	⬇️

Files with missing lines	Coverage Δ
src/ui/layout/BrowseBar.vue	40.33% <ø> (-3.37%)	⬇️
src/ui/router/Browse.js	93.33% <100.00%> (ø)

... and 9 files with indirect coverage changes

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