Most importantly, this can't be emphasized enough:
For best long term health outcomes, 120/70 is the most well substantiated target BP for the vast majority.
It's the lowest hanging health protection measure you can take, with the biggest bang for the buck by a long shot in terms of low effort/high reward. So stick with the trial and error until you find something that gets you to target with no intolerable sides. After that it's one daily pill that you usually don't have to change for years or decades.
With BP meds in general when initiating treatment or changing dose or compound:
It takes 2 weeks to reach the maximum; stable reduction in BP.
It takes a month for the body to acclimate, and side effects to subside (the ones that will subside). Fatigue, occasional light dizzyness, and water retention in the extremities are the most common initially experienced with almost all BP meds until things stabilize. Many people give up prematurely and end up living with "the silent killer" instead. Reassess after a month.
If you're not getting there with 40mg Telmisartan, or any monotherapy BP med, the best strategy is not to increase the dose, which increases the risk and severity of side effects, but to switch to combination therapy of two low dose meds that reduce BP using different mechanisms.
For instance, instead of increasing Telmisartin from 40mg to 80mg, use generic Twynsta, a combination of Amlodipine (a calcium channel blocker) and Telm (An angiotensin blocker) at 5mg Amlodipine / 40mg Telmisartin. That combo has less likelihood of sides than 80mg Telm (or 10mg Amlodipine) while resulting in significantly more BP reduction than either med used alone at double the dose.
All of the "-artan" ARB class BP meds offer advantages and disadvantages. Telmisartan offers more visceral fat reduction, while Valsartan has a more positive effect on libido and sexual function, for instance. Telmisartan improves muscle function, Valsartan improves aerobic performance. They're both banned PEDs in sports, BTW.
I've tried Amlodipine / Telmisartan which increased hair loss for me, so switched to Amlodipine / Valsartan, and not only did the hair loss stop, I love the way the way it makes me feel. That was completely unexpected.
Both one pill combos, 5/80 Twynsta and 5/160 ExForge (the Aml/Valsartan combo brand name) brought me from 160/93 to a rock solid 120/70. (fyi ignore the dosages of different drugs even in the same class. 80mg Telm and 160mg Val are roughly equivalent for instance, there are charts that show equivalent doses to guide you when switching).
If you haven't already, get a home monitor, they're cheap, and keep an eye on your BP closely when trying a new BP med.
Finally, while Telm is widely available from UGL suppliers, it's not difficult to find any of the combo meds from India pharma and easily acquireable in the US with a quick $40 telemedicine call and just telling the provider you had been on (FILL IN BP MED HERE), it was working, but you lost your insurance, and need a prescription so you can get back on it. Use GoodRx to find the pharmacy with cheapest price before the appointment.