So my question is whether I am allowed to report the carryover from last year on the current year's form 1116, even if that carryover will not be used due to the excess credit within the current year itself.
No, you are not allowed to do that.
The excess credits are good for 10 years. They remain separate yearly amounts throughout that 10 years.
If you need to use the excess credits, there is a dedicated line (line 10 on page 2 of 1116) where they may be included. If you need to use more than one year of past excess credits, you may do so, and combine them with other years of excess credits to make up the shortfall of the current year. Note that a detailed calculation explaining how you arrived at the total of excess credits used is required. There is a prescribed format (somewhere) for the detailed explanation. It will include such as the total amount of foreign tax paid applicable
to the basket you are using them for, for that past year (and you may only use past credits from that type of basket), the limitation, the amount of excess credits for that year, how many excess credits are being used to apply to the current year you're considering (you don't have to use all), and what the remainder will be. (There may be more, I don't have past records to hand).
You then have to interpret whether the instructions require filing a 1040X for the year from which you have used the excess credits.