Bought a car in October 2021 in Texas. Didn't claim it as a major purchase last year. Can I claim it this year? Or do I need to Amend my 2021 to recapture the purchase?

You would need to amend the 2021 tax return to add the vehicle as a major purchase for the Sales Taxes.

See this TurboTax support FAQ for amending a tax return - https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-return/amend-change-correct-return-already-filed/L4VjJ9BA2_US_en_US?uid=ld1n99kr

however, amending 2021 will produce no benefit, unless it it increases your itemized deductions or let go change from the standard deduction to itemized.  schedule A taxes are limited to $10,000 (other than married filing separately) so if you have already hit this mark additional sales tax will not benefit you.