[MVS 713] Validate with vue forms

[antxln]

💾 [Code Check]

Make sure you've checked/done the following before making this PR!

• Does your code build/run?
• Does your design approach make sense?
• Does your work achieve the intention of the card?
• Does your code have any unintentional side effects -- have you tested a full workflow & checked the logic branches you touched?
• Did you make a unit test for your code (as appropriate)?
• Is your branch relatively up to date with the Development branch (within ~2 commits)
• Have you moved the card to "Needs QA" in Jira

🐬 [JIRA Sprint Card]

https://mass-immunization-system.atlassian.net/browse/MVS-713

📰 [Work Description]

Validate with vue forms instead of custom methods.

🚦 [Testing/QA Notes]

Consent and screening should work same as before - vaccination proceed only appears when all questions are answered.