Hi there, you are through to Dr. Jake. Im a UK based vet. Im sorry to hear of your concern with you cat. Tallulah.
Her signs of being restless, going in and out of the litter tray frequently and passing only very small amounts of urine are classic signs of her having cystitis. We see this commonly in cats , particularly if they are stressed and her new environment may be a cause of this until she has settled in.
I would recommend making an appointment for her at your local vets so they can perform a full clinical exam , in particular to feel her bladder to make sure nothing else concerning is occurring as stones in the bladder can be palpated sometimes if they are large. Cystitis is often painful so she will require medications to make her feel more comfortable and to help resolve the signs- usually anti inflammatories and often supplements to improve bladder health such as nutra cyst. you vet may also recommend imaging ( x ray or ultrasound) to check the lining of the bladder. As she is in the older age bracket they may also recommend blood tests which would be useful to check all her organs are functioning normally.
the things you can do in the house to make her feel more comfortable include making sure there is multiple litter trays , some more private with hoods, making sure she has access to water, some cats prefer running water. you can try using plug ins such as feliway or nutra calm tablets which can help with the stress until she feels comfortable in her new environment.
further information on this can be seen on this website which is useful and one i provider to cat owners regularly: https://icatcare.org/advice/feline-idiopathic-cystitis-fic/
i hope all this information helps