My experience was pre and during covid, so not recent, but 'might' be helpful. Took 4yrs TTC but sadly MC and GP absolutely useless. In those 4yrs, all they did was a D21 blood test and because it was normal- no gynae referral made! Pregnant a year later and another MC. DH and I were living/working abroad for several months of each year, so we had our fertility work up there.
We/I had:
-The consultant asked about general medical history, our jobs, any previous pregnanies together or with previous partners, any history of STI's, any steroid use, if I had any gynae history such as PCOS, fibroids, menstrual issues etc. These tests weren't all done on site that day, but some were booked in for elsewhere:
-Hycosy to check uterine shape and tube patency. This uses ultrasound but some places still use HSG which is an Xray!
-DH had semen analysis
-We both had STI screening, from memory just via urine samples/blood tests
-Blood tests for thyroid function and general bloods. Also AMH for me to check my egg count which I think was done in combination with an ultrasound.
When I returned to the UK, they accepted all my tests and I was referred to the IVF clinic- which still took at least 6mths from memory. Note that if you are anywhere near the upper BMI limit, wear light clothes and ensure you take your shoes off! Before seeing the consultant, an assistant called me for height/weight, but seemed so rushed, she wouldn't let me get my heavy winter coat off, shoes nor remove a metal knee brace I was wearing at the time!
IF you are considering paying for fertility tests yourself, compare prices with NHS hospitals rather than just private places. I went to guys London and although my 1st round of IVF was NHS, the rest were self funded, but they also offered a full range of fertility testings, hycosy etc and 'might' be better value than say a Harley st equivalent.guysandstthomasspecialistcare.co.uk/services/fertility-prices-and-packages/#investigations
Sorry, I realise this isn't exactly what you wanted to know but hopefully something is useful.