"1. Did you mean to say Schedule 1? " - No, I meant to say Schedule 2. The fact that you did not have a Schedule 2 means that you, without a doubt, did not have a 5329, because any penalty calculated on the 5329 would have flowed to line 8 on Schedule 2. But if there were no numbers for Schedule 2, then the Schedule is not attached to your return (the same is true for schedules 1 and 3).
"2. Can you please clarify what you mean by especially when you're referring to reverse "Unfortunately, the reverse is not true since there are many reasons why there may be numbers on line 8 of Schedule"?" The previous paragraph explains it. The 5329 (look for yourself) has nine parts, each of which calculates a different penalty. If there is no entry on line 8 of Schedule 2, then there is no entry in any part of the 5329. But if there is an entry on line 8 of Schedule 2, all you know is that one or more of the parts on the 5329 showed a penalty, but you don't know which part. So an entry on line 8 of Schedule 2 may or may not show that you carried over excess HSA contributions.
"There's a section that states "Let's enter you HSA contributions". After clicking continue the next page is "Did your employer tell you about any other contributions? Underneath it I clicked yes and then 3 additional prompts popped up: Employer and payroll contributions made in 2022 for the year 2021(This is where I filled out X amount which matches what's on line 8), Employer and payroll contributions made in 2023 for the year 2022, and Employer and payroll contributions not reported in Box-12 of your W-2."
Please UNDO what you did here - You were mixing crabs and apples to get crabapples. Line 8 of Schedule 2 is the penalty for one of several conditions on form 5329 (or did you mean a different line 8?), while "Employer and payroll contributions made in 2022 for the year 2021" is just that - HSA contributions.
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Your post started out with: "It asks to enter last year's excess contribution." I have seen nothing that suggests that you had excess contributions last year (yes, this means for 2021). So just stop and move on from this question and finish the HSA interview.
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