Can you transfer holdings from one account to another

within T212 withthout needing to sell and buy back positions?

No. Investments held in Invest must be sold and rebought in ISA. This is a HMRC rule.

Many other brokers allow positions to be transferred between Invest accounts of spouses. People here have been requested Trading 212 to implement that. Transfer between spouses as a gift is special under UK law because it does not trigger a capital gains tax event and can therefore be useful in balancing out taxable liabilities between spouses.

What about the other way ISA>Invest?

Also has to be done by sale and repurchase. One reason is to establish the new basis cost.