[CAL-5097] add the same "booking questions" to routing forms

[PeerRich]

right now "booking forms" for event-types have more (and different) inputs that routing forms:

event-types:

CleanShot.2025-01-29.at.15.03.49.mp4

routing forms:

CleanShot.2025-01-29.at.15.04.47.mp4

we should reuse the entire event-type booking question UI inside routing forms.

we should also ask for the identifier first and not prefill it. (see event-types)

_CAL-5097

[PeerRich]

/bounty 50

[algora-pbc]

💎 $50 bounty • Cal.com, Inc.

Steps to solve:

1. Submit work: Create a pull request including /claim #18987 in the PR body to claim the bounty
2. Receive payment: 100% of the bounty is received 2-5 days post-reward. Make sure you are eligible for payouts

Thank you for contributing to calcom/cal.com!

Add a bounty • Share on socials

[PeerRich]

its important that we only maintain one set of custom inputs, which means adding a new input type to event-types will also add it to routing forms

the systems should not be maintained individually

[algora-pbc]

💡 @oliverqx submitted a pull request that claims the bounty. You can visit your bounty board to reward.