Do a more complete mode switch from switch_mode command

[mrubens]

From Discord: "found a bug. When I approved the mode change it doesnt change the model like it does when i manually switch"

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Important

Fix mode switch bug by centralizing logic in handleModeSwitch() in ClineProvider, ensuring correct API provider updates.

• Behavior:
  • Fix bug where API provider wasn't updated after mode switch in Cline.ts and ClineProvider.ts.
  • Introduce handleModeSwitch() in ClineProvider to centralize mode switching logic.
• Tests:
  • Add tests for handleModeSwitch() in ClineProvider.test.ts to verify correct API config loading and saving.
• Misc:
  • Update Cline.ts to use handleModeSwitch() for mode changes.

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