Re: "DuckDuckGo becomes unresponsive in Safari". "It's the only website that seems to have this issue".
Wondering if DuckDuckGo is your default search engine:
Choose a search engine for Safari on Mac - Apple Support
and
if so, what happens if you type your search terms in the Safari URL / "Smart Search" field, instead.
or
If not, maybe the default search engine is conflicting somehow. (You could experiment by using that to search.)
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Re: "The page often locks up, at which point it doesn't allow me to scroll, click on a link,
or type in the search box on the webpage".
Am assuming "the page" is the DuckDuckGo webpage itself, the one with the search field.
Wondering if you may accidentally: Lock private browsing windows in Safari on Mac - Apple Support
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Re: "Is this happening to anyone else"
All seems as normal on my Mac using DuckDuckGo with same MacOS and Safari version (am in Australia).
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Re: "is there a way of fixing this issue?"
Troubleshoot:
Try making DuckDuckGo your default search engine, and just enter your search terms in the Safari URL field
or
You could check whether DuckDuckGo is down / has problems / if it becomes unreliable again:
(Choose your country by clicking on the tiny globe with "US" under in the top menu of linked webpage below.)
https://downdetector.com/status/duckduckgo/
If needed: Safari Support webpage (info. / support / contact options etc.)
Safari - Official Apple Support
All the best :-)