Relocation, Remote Work, Contracts and Taxes

Good afternoon. I am in a tricky situation this year and I'm wondering how much I should plan to put aside for taxes in the spring. My situation:

  • Worked a full-time job through May 7 in one state
  • From May 10-31, I worked part-time for the same company — May 10-26 in one state, May 26-31 in another.
  • Meanwhile, I started a new full-time job that's fully remote on May 10 and worked it in SC until May 26
  • On May 26, I relocated to a new state and continued my new full-time work upon arrival.
  • From June 1-August 30, I did untaxed contract work remotely in my current state.

All my full-time and part-time work had taxes taken out. Between different work classifications and states, plus total income, what I need to do to prepare is clear as mud, especially when consulting the IRS website. Without actual numbers and states detailed here, can anyone offer any clarity on what I should set aside?