Extract current mode from home fragment

[NotWoods]

Pulls out the function for getting the current mode and emitting when it changes. Long-term this should probably be moved to some state for the home fragment.

Pull Request checklist

• Quality: This PR builds and passes detekt/ktlint checks (A pre-push hook is recommended)
• Tests: This PR includes thorough tests or an explanation of why it does not
• Screenshots: This PR includes screenshots or GIFs of the changes made or an explanation of why it does not
• Accessibility: The code in this PR follows accessibility best practices or does not include any user facing features

After merge

• Milestone: Make sure issues finished by this pull request are added to the milestone of the version currently in development.

[codecov-io]

Codecov Report

Merging #5343 into master will increase coverage by 0.24%.
The diff coverage is 50%.

@@             Coverage Diff              @@
##             master    #5343      +/-   ##
============================================
+ Coverage     12.89%   13.14%   +0.24%     
  Complexity      283      283              
============================================
  Files           252      253       +1     
  Lines         10362    10363       +1     
  Branches       1504     1506       +2     
============================================
+ Hits           1336     1362      +26     
+ Misses         8936     8911      -25     
  Partials         90       90

Impacted Files	Coverage Δ	Complexity Δ
...nix/home/sessioncontrol/SessionControlComponent.kt	1.35% <ø> (+1.35%)	0 <0> (ø)	⬇️
.../fenix/home/sessioncontrol/SessionControlUIView.kt	0% <ø> (ø)	0 <0> (ø)	⬇️
...fenix/home/sessioncontrol/SessionControlAdapter.kt	0% <ø> (ø)	0 <0> (ø)	⬇️
...c/main/java/org/mozilla/fenix/home/HomeFragment.kt	0% <0%> (ø)	0 <0> (ø)	⬇️
app/src/main/java/org/mozilla/fenix/home/Mode.kt	100% <100%> (ø)	0 <0> (?)

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[sblatz]

Manually tested:

• Onboarding gets dismissed properly
• Onboarding updates correctly based on account login
• Private mode switching works

Looks good, thanks for all the tests!!