Is self bought health insurance paid for by the taxpayer eligible for any tax credit or break in 2023 filings? not obamacare but insurance purchased by self

It can be added to your Medial Expenses and a portion may be deducted on Schedule A if you Itemize Deductions. 

If you use the Standard Deduction, the expense will not be reported. 

If you are itemizing deductions like mortgage interest, property tax, etc. then you can enter the health insurance premiums you paid as a medical expense.   Your question is posting from the Free Edition---which does not support itemized deductions.   Unless you have enough itemized deductions to exceed your standard deduction, you will not want to trigger an upgrade to Deluxe by entering medical expenses etc.  

MEDICAL EXPENSES

The medical expense deduction has to meet a rather large threshold before it can affect your return. The amount of medical (including dental, vision, etc.)  expenses that will count toward itemization is the amount that is OVER 7.5% of your adjusted gross income. You should only enter the amount that you paid in 2023—do not include any amounts that were covered by insurance or that are still outstanding.  Of course, your medical expenses plus your other itemized deductions still have to exceed your standard deduction before you will see a difference in your tax due or refund.

To enter your medical expenses go to Federal>Deductions and Credits>Medical>Medical Expenses

2023 STANDARD DEDUCTION AMOUNTS

SINGLE $13,850  (65 or older/legally blind + $1850)

MARRIED FILING SEPARATELY $13,850  (65 or older/legally blind + $1500)

MARRIED FILING JOINTLY $27,700  (65+/legally blind) )  + $1500 per spouse

HEAD OF HOUSEHOLD  $20,800 (65 or older/blind)  + $1850)