Is the prayer of one who recites the middle Tashahhud in the Friday prayer by mistake accepted, and he forgot to send blessings upon the Prophet (peace and blessings be upon him) and seek refuge?

Your prayer is valid, and you are not required to repeat it for omitting the prayer upon the Prophet (peace be upon him) in the last tashahhud (definition), according to most scholars. Al-Mughni mentioned that praying upon the Prophet in the last tashahhud is obligatory in the sound view of the Hanbali madhhab (definition), and this is also the opinion of Al-Shafi'i and Ishaq. However, Malik, Al-Thawri, and most scholars held that it is not obligatory, a view supported by Ibn Al-Mundhir, who stated that this is the opinion of the majority of scholars, except for Al-Shafi'i.