Plans 2023: Update with-theme flow to use intent for plans

Related to https://github.com/Automattic/wp-calypso/pull/77667 , https://github.com/Automattic/wp-calypso/issues/77187

As of https://github.com/Automattic/wp-calypso/pull/77667 we are showing the tailored flow's plans when visiting /plans with a site created in respective tailored flow. This is done via the use of "intent" in place of tailored plans lists passed from signup or admin.

Similar to hosting flow, the flow under `/start/with-theme` should migrate to use this new framework. This should lead the way to start cleaning up the use of [conditional props](https://github.com/Automattic/wp-calypso/blob/trunk/client/signup/steps/plans-theme-preselected/index.tsx#L27-L49) (`hidePersonalPlan`, `hideFreePlan`, etc.) to hide specific plans from the default list. Let's investigate if these can be refactored easily to use a specific "with-theme" intent instead.

Start by reading the related PR 77667 and issue 77187, then trace the /start/with-theme flow and the conditional props in client/signup/steps/plans-theme-preselected/index.tsx. Migrate the flow to use the intent framework and verify that visiting /plans for a site created through with-theme shows the intended plans without relying on unnecessary plan-hiding props.

Written by the indexing model from the issue text.