When you enable Mate's Safari extension, Safari warns that Mate can "read and alter webpages and see your browsing history". Chrome, Firefox and Edge show a similar warning for the browser extension.
Why
To translate text on a page, Mate has to run a small script on that page: to show the floating button next to your selection, to open the tooltip, and to replace the page text during full-page translation. Safari grants that ability with this permission; there is no narrower one. "Browsing history" is Safari's way of saying the extension can know which page you're on, which it needs to know where to inject the script.
What Mate does with it
Mate reads only the text you select or the page you ask to translate, and sends only that text to the translation engine. It doesn't record which sites you visit, doesn't collect page contents, and doesn't sell or share anything. See What data does Mate send and store? and the privacy policy.
If you'd rather limit it
Safari lets you allow the extension per website: in Safari › Settings › Extensions › Mate, choose the sites, or pick "Ask" so Safari checks with you on each new site. Mate then works only where you've allowed it.