Install https://addons.opera.com/en/extensions/details/user-agent-switcher-5/, click its icon on the address bar or in the cube icon's submenu, set it to Chrome for Windows, click the edit button (the pencil icon) and set the user agent string to:

Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/114.0.0.0 Safari/537.36

Then, goto the URL opera://settings/content/all, type mobile01.com in the search field and click "Clear displayed content".

Then, goto the URL opera://settings/clearBrowserData and clear "cached images and files" for all time.

That should cause the site to thinking you're using an updated version of Chrome instead of Opera.

If that doesn't help, in addition to that extension, each time you start Opera, goto the URL opera://browserjs and disable browser.js for the session to see if it helps.

If nothing helps, there's a chance that the site depends on support for something that Opera 95 doesn't have.