Is dedicating a specific time after the Friday 'Asr prayer for worship, such as dhikr, tasbeeh, and sending blessings upon the Prophet (peace be upon him), considered an innovation (bid'ah)?

The Prophet, peace and blessings be upon him, warned against innovations and clarified that the morning and evening remembrances (adhkar) are legislated. Texts have indicated the importance of being assiduous in performing them, and they can be found in Hisn al-Muslim and other books of adhkar.

Accordingly, these remembrances are legislated to be recited after Asr. If you are preoccupied with memorizing and studying the Quran, there is no harm in dedicating Friday to performing them, because remembrance and supplication are legislated at this time, and the hour of responsiveness on Friday is the last hour after Asr.