Good news on your first question: Freetrade will collect the basic-rate tax relief directly from the government and put it into your account when you make the contribution, they don’t wait until the end of the year. They say “It normally takes around 6-11 weeks from the contribution to the tax relief appearing in your account” (Open SIPP - Self-invested personal pension account | Freetrade). You can then invest the additional money.
As a higher rate taxpayer, you’ll make an additional claim on your tax return. There’s a box labeled “Payments to registered pension schemes where basic rate tax relief will be claimed by your pension provider” – enter there your total contributions plus the basic rate tax relief you’ve already received (read the instructions carefully and pay attention to gross versus net contributions).
And yes, you should keep an eye on your annual total of all pension contributions, to your workplace pension and to SIPPs, to make sure you don’t go over the limit. If you’re a higher rate taxpayer and making contributions through your employment, that could happen without you noticing if you don’t watch out for it, but you might be able to compensate by using unclaimed allowance from previous years if you’ve contributed less than the maximum in the past.