Given the minimal usage of the option, this will only impact a relatively small number of websites. But that, of course, could be your site - today, Twitter has announced that, due to low usage, it's retiring the Likes, Collections and Moments embeddable timelines as of June 23rd, 2021.
Many websites include an embedded listing of their tweets (like these examples above) to help connect users to their Twitter presence, and keep visitors up to date on their latest tweet commentary. But most of those embeds, Twitter says, are home or list displays.
"During our analysis, we discovered the overwhelming majority of users choose to embed Profiles or Lists: comprising 99.48% of domains that embed timelines. Only 0.52% of domains who embed Twitter timelines use the Likes timeline, Collections timeline, and Moments timeline."
So hardly anyone is using these alternate timeline displays. As such, it makes sense for Twitter to stop supporting them.
"Because of the low usage for the Likes, Collections, and Moments timelines, we plan to retire them on June 23, 2021. This change will not affect the more than 99% of people using embedded timelines, and we will continue to focus on delivering value through our more utilized Profiles and Lists timelines."
So, likely no big deal for your website - but if, for some reason, you are currently displaying a real-time feed of the tweets you've liked on your website, soon, you won't be able to.
You can probably switch to a home feed instead, or remove the tweet widget entirely. In any event, it may be worth reviewing any embedded tweet feeds on your site to ensure you won't be impacted.
You can read more about Twitter's coming update here.