1st and foremost pls bear in mind that not only do things change here all the time it is sometimes without notice and each application seems to follow its own path :-/ Any advise given would only be applicable to that case and at that point in time! Also depends on if you have a EU passport or not. Even the professional immigration companies do not know some of the changes that have just been made!
Given the swerves that immigration throw your way I would recommend that you engage a professional unless you have a lot of time on your hands and you enjoy the frustration of immigration! They will ask for things and then when you arrive they want more things they never asked for. Appointments are or have been very difficult to get and professionals already have these in place. You need an appointment agreed in writing by the return email from immigration before the 90 days expires. With the appointment email you can exit and return to Cyprus without having an issue with the boarder police. Cost varies and I have seen 750 to 2000 eur depending on complexity. You need to gather all the documents you can before leaving the UK. A professional will tell you what is required like ACRO police clearance, birth certs, marriage/divorce papers and all argininal or certified and some apostilled. If you look at other post on this forum you will see what WAS required. Then on arrival things like x-rays, rental agreement house purchase details etc. There will be a lot to deal with and anything you can do to reduce this burden is worth investing in.
Also things here are very very slow! I applied for my temp visa in Dec 2022 and recvd the papers in March 2023 after many visits to the immigration office with the professional. My vehicle custom's clearance took 14 months to complete. You will need to open a Cypriot bank account as this is the only option and this took me about 2 weeks and 3 visits standing in line. total time probably 9 hours in the bank. Do not expect things to be like the UK as email and web sites do not get results here you will need to go and have a face to face meeting with anyone you need to interact with. Emails get ignored and phone call never get answered.
On the bright side it will all be worth the effort as life is Soooo much better here doctors, dentists and hospitals just work and see you immediately rather than months of waiting.
Just ask any question you have as there is lots of experience on this forum.
