It depends on the app. Freetrade puts the share in your general investment account (GIA), and Lightyear requires a GIA for monetary rewards, so those shares sit outside the ISA tax shelter. Trading 212 credits the share to the account you opened and funded, which can be a Stocks ISA; only SIPP rewards are paid into an Invest account instead. The ISA allowance for 2026/27 is £20,000; if the share lands in an ISA, ask Trading 212 whether it counts toward it.
HMRC has not published guidance specific to promotional free shares, and the apps say tax is your responsibility. Gains on shares held outside an ISA fall under capital gains tax, which has a £3,000 annual exempt amount. Keep the award records with your other investment paperwork.