Use underscore prefix consistently for private JS members

[jotaen4tinypilot]

According to our coding conventions, all (supposed-to-be) private JS members should have an underscore prefix.

• I think we are fairly consistent in regards to naming methods here, but it would be good to double-check this anyway
• For fields, we have non-prefixed ones, e.g. in <remote-screen>. So we should check all components.
• The conventions around our common identifiers this.state and this.elements need to be updated to this._state and this._elements, and all code refactored.

We also have to do this in Pro.

[jdeanwallace]

From a recent meeting with @mtlynch, to keep this task a small we've limited the scope of this task to the following changes:

• this.elements => this._elements
• this.state => this._state
• this.states => this._states
• this.statesWithoutDialogClose => this._statesWithoutDialogClose

The outstanding remaining changes are less uniform and might be tedious/time-consuming to review.

[jdeanwallace]

Completed via

• https://github.com/tiny-pilot/tinypilot/pull/1758
• https://github.com/tiny-pilot/tinypilot/pull/1759
• https://github.com/tiny-pilot/tinypilot/pull/1760
• https://github.com/tiny-pilot/tinypilot/pull/1761