To correct an excess Roth IRA contribution you can either request an explicit return of contribution or by recharacterization of the contribution to be a traditional IRA contribution (possibly nondeductible) instead. The returned or recharacterized contribution is accompanied by the attributable investment gain, which should be calculated by the Roth IRA custodian. The deadline to do either of these is the due date of your 2023 tax return, including extensions.
Once that is done, yes, you will need to amend your 2023 tax return if it has already been filed.
The term "Roth conversion" has different meanings depending on the context. The tax code defines it as only the movement of funds from a traditional IRA to a Roth IRA. The movement of funds from a traditional account in a qualified retirement plan to a Roth account is called a taxable rollover and, if done to the designated Roth account in the plan, is called an IRR, as you mentioned. However, because of the similarities in moving funds from a traditional account to a Roth account in a taxable transaction, common usage tends to apply the term "Roth conversion" to all of these.
