You hosted the business or portfolio video on Vimeo Free because you were already familiar with it, and because the player does not run ads. Then a file on your website stopped playing for visitors.
A library that only has to play needs a different host from a video that has to sell. TrackPlay leads this list when the video has to sell on traffic you pay for. Wistia is the host to open when you only need more embed storage at no charge.
Work out what this video costs after you leave the free allowance. The three inputs are length, visitors and how much of the video they watch.

A free alternative to Vimeo that you can stay on
The Free plan caps embeddable and non-public storage at 3 GB. Public videos that are not embeddable have no storage limit. The embedding article says every embeddable video counts toward that cap, even a public one. Files embedded on your website draw from that allowance.
The same Free plan page includes 1 TB of bandwidth a month for embeddable and non-public video, resetting at the start of each billing month. Public videos that are not embedded do not use that bandwidth. On a typical business site, storage runs out first.
That page also says there are no ads before, after, or on the video. A portfolio stays on Vimeo for that reason.
Once your library exceeds the cap, Vimeo restricts the newest files first, until the library is back under the limit or you upgrade. The lapse FAQ explains that order. It also says Password, Unlisted and embed-only videos are changed to Private, so a password link or a hidden embed stops working for visitors.
Background embeds and chromeless layouts, which hide the player interface, are paid. So is hiding the Vimeo logo, the play bar, the volume control and the fullscreen button. The Free plan keeps the logo. Both points are in the embedding article.
On one r/vimeo thread, a creator with about 2 to 3 GB of video was told to see whether another host's free storage would cover it. On a portfolio thread, people point those embeds at Wistia's free tier.