I've worked in companies where change aversion made it difficult to migrate legacy codebases onto anything more modern or efficient. It's not uncommon to hear stakeholders use the "if it's not broken, why fix it?" rationale. They often don't have your insight into the maintainability of performance issues some of these decisions can cause over time.
One approach I've increasingly found teams use is pitching for an A/B test - e.g "Let us try to migrate over a smaller part of the site. If we can show you it will improve business/conversion metrics by at least X, let us try it out for other parts of the site". This reduces the cost of the exploration in the eyes of the business ("they're just asking to do this for one page or section...") and gives you a target to justify continued investment.
Where it's not quite as straight-forward as demonstrating a change will lead to improvements in business metrics, showing data about how many engineering hours will be saved by switching to a more modern Magento vs maintainance cost of old, what other opportunities doing so unlocks etc might also be something that can convince the business it's worthwhile letting you explore it.
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