Vlad Good question. I looked a bit into it, this seems to be the definition of the format. The part directly after the "part of speech" header is the definition. Maybe return the first ~3 of these definitions, depending on the character length of the definitions. And then add the synonyms, amount does also depend on the length of the synonyms.
Just extracting these information returns a text that could fit into 300px (with some better formatting and whatnot than this plaintext representation).
Definitions:
1. An adult female human.
2. (collective) All female humans collectively; womankind.
3. A female person, usually an adult;
a (generally adult) female sentient being, whether human, supernatural, elf, alien, etc.
Synonyms:
lady;
female;
see more at Thesaurus:woman
After this, link back to the Wiktionary for a complete list and more information.
I also found some other links/hints, which I don't know if they are of any interest to you.
Wordnik https://www.wordnik.com/about is a third party API that includes Wiktionary and other dictionaries, also includes audio which could be interesting for https://kagifeedback.org/d/321-word-pronunciation/5.
To take a look at the underlying format of the Wiktionary entry, you can use:
view-source:https://en.wiktionary.org/w/index.php?title=woman&action=raw
To get the Wiktionary link (if any) for a Wikipedia page, https://en.wikipedia.org/w/api.php?action=parse&prop=iwlinks&page=MVP
This script (now defunct) returned the first definition as HTML via this API endpoint:
https://en.wiktionary.org/w/api.php?action=parse&prop=text&format=xml&xslt=MediaWiki:extractFirst.xsl&page=Word
This uses some kind of XLS file that only parses the first definition:
https://en.wiktionary.org/wiki/MediaWiki:ExtractFirst.xsl