Libido can be a difficult area because there can be many, many inputs involved. It's not just testosterone.
Broadly, there are many types of adverse health status or deficiency that for many individuals can harm libido. Vitamin D deficiency, iodine deficiency, metabolic changes mentioned in next paragraph, high or low corticosteroid levels, "adrenal fatigue," disrupted or desynchronized circadian rhythms, prolactin level, dopamine production, and high or low estrogen levels can all harm libido.
The metabolic changes I refer to are slowed metabolism and reduced insulin sensitivity (progression along the prediabetes/diabetes path) and progression towards obesity.
I'm not saying all that to be a downer but rather to be clear that testosterone alone is not the whole story, which can explain why T replacement alone has not been doing the job for you.
Sort of going down that list:
Do you get a lot of strong sun on a fair amount of skin, or take Vitamin D at at least, for example, 2000 IU per day? If so then Vitamin D deficiency is unlikely. If not, then a 25-hydroxy Vitamin D test could be called for.
Does dairy, eggs, seafood, baked potatoes with skin make up a quite substantial part of your diet, or do you use iodized salt fairly plentifully, or do you take an iodide-containing supplement? If yes, then iodine deficiency is I think unlikely; if no then it's fairly likely. A urine test can be done which is the most accurate method, or you could simply improve your intake of the above. If desired, up to 2 mg/day of iodide supplement or corresponding amount of iodized salt could be used for a couple of weeks to quickly restore levels if deficient, and will not harm if not deficient. A thyroid panel should be run as well in any case.
Corticosteroid levels are determined by blood test. "Adrenal fatigue" where corticosteroid levels are normal is an area that I don't consider myself expert in and can advise only reducing or eliminating stimulant usage, reducing exercise if excessive for the condition, improving nutrition, and reducing stress in general.
If you tend to awake to eat, you almost certainly have desynchronized circadian rhythms. If you sleep pattern is typically disrupted or you do shift work, it's also likely.
Prolactin is measurable by blood test.
Dopamine. I view by whether there's improvement with pramipexole or selegiline (pramipexole will also lower prolactin.)
Estrogen: determined by estradiol blood test.
Also relevant of course is what your free testosterone is on your TRT protocol.