The E & W cisgender population is 59.6 million – the cisgender prison population is 87,900 = 0.15% of people in E & W are in prison.
The E & W trans population is 262,000 – the trans prison population is 268 = 0.1% of trans people in E & W are in prison.
From this statistic, we learn that cisgender people commit crimes at a 50% higher rate than trans people.
Evidence from the research conducted by Olga Suhomlinova and Saoirse Caitlin O’Shea using official statistics dating from 2021 revealed that while 0.5% of the population identify as transgender or non-binary, they represented just 0.2% of the prison population.
Transgender People, Crime and Prisons – Trans Women & Trans Men
Another anomaly in the statistics is that while 96% of the cisgender prison population is male and 4% female, the trans prison population is 84% trans women and 16% trans men.
It's absurd to lump all so-called 'cisgender' people together when there is such a discrepancy in the numbers of males and females in prison.
Of that 87,900 people in prison, only 3,516 are female and the remaining 84,384 are male. Assuming the number of males and females in the general population are equal, that means that about 0.28% of men are in prison, but only 0.01% of women.
Similarly for the trans prison population (assuming here that there are equal numbers of trans people of each sex).
Using your figures there are about 43 TIFs in prison and 225 TIMs. So respectively 0.03% of the TIF population is in prison and 0.17% of the TIM population.
This means that trans identifying females are about 3 times more likely than other females to be in prison. For males, the trans identifying population is less likely than other males to be in prison, but about 17 times more likely than females. The TIM offending rate is much closer to the male rate than the female rate.
Of course, as @PermanentTemporary pointed out, the trans population was grossly over-estimated in the census, which could mean that the criminal rate for trans identifying men is even closer to that of other men.