I know that metals have the capability to lose electrons and form cations, but is it also theoretically possible to supply an electron to a metal so that it forms an anion?
If so, has it ever been done?
I referred this question (Can two metals combine to form a compound?) but could not get a satisfactory solution from that.
Absolutely! You will find these mostly in electride systems and off these, mostly in alkali metals. Here is an example research paper:
"Superakali-Alkalide Interactions and Ion Pairing in Low-Polarity Solvents, J. Am. Chem. Soc., 2021, 143(10), 3934–3943 (https://pubs.acs.org/doi/10.1021/jacs.1c00115)
Remember, metals have a positive charged when ionized because it is energetically more favorable to lose electrons than to gain them, this being of course an oversimplified version of electron orbitals and shells. If you have a situation in which this is reverse or not possible, you will get a negative metal ion
The electron affinity, defined as the energy released in the reaction
$$\ce{X(g) + e^- -> X^- (g)}$$
is positive for all but the noble elements and a few elements with half-filled shells (see a data table here), which is consistent with the anion being more stable than the neutral atom. This makes it difficult to understand the motivation for the first half of your question, since the answer is a resounding yes, there is no spontaneous driving force that would drive (most) isolated metal anions to dissociate giving up an electron. There is at first glance no theoretical basis to suppose such anions cannot be formed.
On the other hand, the ionization energy of all (gas phase) atoms is positive, that is, loss of an electron is an unfavorable process. So it is not a good idea to generalize that "metals have a positive charge when ionized because it is energetically more favorable to lose electrons than to gain them". Just the opposite. Most metals have favourable electron affinities.
Making anions that are stable is another matter, precisely because most other elements also attract additional electrons.
A useful measure of the relative attraction of elements for electrons is the electronegativity, of which the Mulliken variant is defined as an average of the first electron affinity and ionization energies. And since metals have smaller electronegativities than non-metals, they tend to lose electrons rather than gain them. While most metals have positive electron affinities, their ionization energy is often lower than the electron affinity of other atoms.
Yes, there are a large number of negatively charged metal ions, many of them containing several covalently bound atoms. The positively charged counterion is typically a group 1 metal.
Wikipedia defines a zintl phase as the product of a reaction between a group I or group II metal, and a post transition metal or metalloid, but most of the examples are based on elements that are not unambiguously metals (such as silicon.)
https://en.wikipedia.org/wiki/Zintl_phase
There are however separate pages for plumbides and stannides. The stannide page claims Sn(4-) in Mg[2]Sn which is a surprising amount of charge on one atom. Polymeric (Sn(2-))[n] has more reasonable double negative charge.
https://en.wikipedia.org/wiki/Plumbide https://en.wikipedia.org/wiki/Stannide
To make a capacitor out of metal, you have to have negatively charged metal atoms on one of the plates (although I guess one could argue that the negative charge is not tied to a particular atom, but shared among all the atoms).
