[Remove Vuetify from Studio] Buttons, dropdowns, and dialog in channel editor root page

[vtushar06]

Summary

Migrated channel editor toolbar from Vuetify to KDS components, replacing VTooltip, VBtn, VList, and BaseMenu with KDS equivalents.

Changes:

• Replaced VTooltip with KTooltip (error count + publish button tooltips)
• Replaced VBtn with KButton for Publish button
• Replaced BaseMenu + VList with KButton + KDropdownMenu for Share dropdown
• Replaced VBtn + BaseMenu + VList with KIconButton + KDropdownMenu for three-dots menu
• Added shareMenuOptions and channelMenuOptions computed properties
• Added handleShareMenuSelect and handleChannelMenuSelect methods

Screenshots:

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References

Closes #5597
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Reviewer guidance

1. Login as [email protected] / a
2. Go to Channels > Published Channel > Edit (to enter channel editor)
3. Test Share dropdown (desktop view)
4. Test Publish button
5. Test three-dots menu
6. Test responsive behavior (resize browser to mobile width ~375px)

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