Is it permissible to say, "I seek forgiveness from Allah, the Almighty, Whom there is no god but He, the Ever-Living, the Sustainer, and to Him I repent, (forgive me) to the extent of His creation, to the degree of His pleasure, by the weight of His Throne, and by the ink of His words," and other adhkar in a similar format?

Adhkar (remembrances of Allah) are divided into restricted and unrestricted categories. Restricted adhkar do not permit addition or subtraction from their wordings, such as the morning and evening adhkar. As for unrestricted adhkar, this is permissible for them.

The formula (as many as His creation, as pleases Him, as much as the weight of His Throne, and as much as the ink of His words) was mentioned in tasbeeh (glorification of Allah) and was authentically established in a sound hadith (definition) from Juwayriyah (may Allah be pleased with her). It also appears in another hadith alongside tahmeed (praising Allah), takbeer (magnifying Allah), tahleel (declaring Allah's oneness), and hawqalah (saying 'La hawla wa la quwwata illa billah') in another hadith.

As for istighfar (seeking Allah's forgiveness), it is among the unrestricted adhkar. There is no harm in seeking forgiveness with the mentioned formula, (I seek Allah's forgiveness as many as His creation...), for it is permissible and there is no dislike for it. However, it does not have a specific merit established for it except with proof. It is more preferable to limit oneself to the forms of istighfar in the Sunnah (definition), such as (My Lord, forgive me and accept my repentance, verily You are the Oft-Forgiving, the Most Merciful), or "Sayyid al-Istighfar" (the master of seeking forgiveness) which the Prophet (peace be upon him) taught us.