Form 1040 Line 8 is taken from Schedule 1 Line 9. Many items are added together, including unemployment and its exclusion and business income.

the instructions for form 1040 (page 87 in the IRS instructions) specifically states for line 8 "For tax year 2020 line 8 will be used to report unemployment compensation exclusion as figured on the unemployment compensation exclusion worksheet. It then goes on to say Caution "Do not report on this line any income from self-employment or fees received as a notary public. Instead, you must use Schedule C, even if you don't have any business expenses. Also, don't report on line 8 any non employee compensation shown on Form 1099MISC or 1099 NEC.  My business profit is on line 31 on Schedule C and on line 3 and line 9 on Schedule 1. These are then being transferred to line 8 on the 1040. Do you see my confusion?

No. Line 3 Schedule 1 receives this income from Line 31 Schedule C. Line 3 Schedule 1 is combined with all the other income in Part I and flows to Line 9. The amount from Line 9, Schedule 1 flows to Line 8 1040. If you read each line on each form, you will see that how that happens.

You said, "The IRS instructions for that line this year specifically says For tax year 2020 line 8 will be used to report unemployment compensation exclusion.". It never says the only thing reported there is unemployment exclusion.