I'd be surprised if surgery itself increased the suicide risk by 7%. If there were truth in that I think the NHS would have put the brakes on it a long time ago
I don't think so, because we are talking about a small increase in the rate of suicide in a relatively small number of people.
From the latest ONS release:
In 2019, there were 5,691 suicides registered in England and Wales, an age-standardised rate of 11.0 deaths per 100,000 population.
I don't know what is the total number of trans people in the UK who have undergone GRS, but I presume it is a few thousand.
Assuming a population of 10,000 such trans people (to keep the figures simple), if the rate of suicide in this group were the same as in the general population, then there would be approximately 1 per year (1 tenth of the number for 100,000 in the general population gives 1.1 per year). Increase this by 7% and it becomes about 1.18 people per year. The numbers are so small that it would be difficult to draw any conclusions, since 2 or 3 suicides in one year would skew the figures enormously, but might be due to completely different reasons than anything to do with their surgery or the fact that they are trans. It would also be skewed if there were no suicides one year, even though this is very likely in this small number of people.
The 20x figure mentioned in the OP is a completely different matter. But it's reported in that paper that:
Despite the long history of this treatment, however, outcome data regarding mortality and psychiatric morbidity are scant. With respect to suicide and deaths from other causes after sex reassignment, an early Swedish study followed 24 transsexual persons for an average of six years and reported one suicide.[5] A subsequent Swedish study recorded three suicides after sex reassignment surgery of 175 patients.[6] A recent Swedish follow-up study reported no suicides in 60 transsexual patients, but one death due to complications after the sex reassignment surgery.[7] A Danish study reported death by suicide in 3 out of 29 operated male-to-female transsexual persons followed for an average of six years.[8] By contrast, a Belgian study of 107 transsexual persons followed for 4–6 years found no suicides or deaths from other causes.[9]
At the moment, we just don't have enough data (although the numbers in the above paragraph do generally seem quite high for such a small number of people over a short period of time).