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Dear @Jaden Joshua Amatuzzo,
Thank you for taking the time to provide such a detailed report, along with a clear minimal reproducible example. The comparison between the inline LAMBDA and the named LAMBDA behavior is especially helpful for troubleshooting.
Based on the behavior you described, it appears that when a LAMBDA containing an INDEX function with an array-valued row_num or column_num argument is saved in Name Manager, Excel may not consistently recognize the result as an array when it is passed to another function. Although the named LAMBDA correctly spills the expected values, functions such as SUM() and COLUMNS() may treat the result differently than they do when the same LAMBDA is evaluated inline.
Since the issue is reproducible in Excel for the Web and not consistently reproducible across all environments, this behavior does not appear to align with the expected results demonstrated by the inline LAMBDA examples you provided.
At this time, the behavior suggests a potential issue within the Excel calculation engine rather than a problem with the formula syntax itself. To assist with further investigation, I sincerely recommend you try to create a support ticket from: Microsoft 365 Admin Center > Support > Help & Support. You can raise support ticket from: https://admin.microsoft.com/#/support/requests
The support team over there has higher permission than us to investigate the issue from background, they have more resource and correct escalation channel in handling this kind of issues. This would be a more efficient way in handling the case for you.
For reference: Get support | Microsoft Docs
Thanks for your patience and understanding so far. Hope you having a nice day and really much warm regards to you as well!