Is it permissible to adopt the view that considers the takbir (Allahu Akbar), the oath, and the slaughtered animal valid when uttered by someone who omits the letter "ha" from the name of Allah, especially for the one who suffers from obsessive doubts?

The cure for waswasah (whispers/obsessive thoughts) is to turn away from them and ignore them, and to consult mental health professionals. Some scholars have mentioned that it is permissible for a person afflicted with waswasah to adopt the lightest and easiest of scholarly opinions. As for omitting the letter hā’ from the word Allah (the Glorious Name), there is no hardship in pronouncing it. The general consensus among scholars is that prayer and other acts of worship are not valid if the hā’ is omitted. However, some later Hanafi scholars mentioned that an error in pronouncing letters does not invalidate the prayer if it is a widespread affliction (‘ammat bihi al-balwā). Nevertheless, one should not be lenient in articulating the hā’ perfectly under the pretext of there being a difference of opinion.