Why was I supposed to get $1,678 back in federal refund, but I only recieved $1,276?

Is the amount sent/issued by the IRS the same as the refund amount shown on your federal tax return Form 1040 Line 35a? - https://www.irs.gov/refunds

If not, then go to this IRS website for information on reduced refunds - https://www.irs.gov/taxtopics/tc203

Are you also receiving a state tax refund? If so, the state refund is sent directly to you based on how you chose to receive the state tax refund, it does not go through the third party processor.
Use this TurboTax support FAQ to check the state tax refund status - https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

Have you factored in the TurboTax account fees and the TPG service charge of $40 plus any applicable sales tax?
Review your TurboTax account fees -
Sign onto the TurboTax website with the User ID you used to create the account - https://myturbotax.intuit.com/
Scroll down to the bottom of the screen and on the section Your tax returns & documents click on View Order Details

If you requested to have the TurboTax account fees deducted from your federal tax refund, the IRS will send the refund to a third party processor to have the fees and the $40 service charge deducted. The third party processor will deduct the TurboTax fees plus the $40 service charge and then attempt to direct deposit the remaining refund balance into the account that you entered on your tax return.

For the status of your tax refund you will need to contact the third party processor, Santa Barbara Tax Product Group, using their website - https://www.sbtpg.com/

Tax Products Group Contact Information - https://help.sbtpg.com/hc/en-us/articles/230084587-Contact-Information

Call 1-877-908-7228

Or email - TPG-CSsupport@greendotcorp.com