If you're looking to convert that to HTML, then yes, there is the
action=parse API. For example:
https://en.wiktionary.org/wiki/Special:ApiSandbox#action=parse&format=j…
If you want to turn that into machine-readable data, or to extract the
conjugations from other pages, then there is probably no way to do it,
other than implementing it on your own.
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Bartosz Dziewoński