I tried to make myself easier by trying to recall albums where more than one best song were covers. That narrows the choice.
Eric Clapton - 461 Ocean Boulevard - (at least) 2 best
Motherless Children (trad)
I Shot the Sheriff (Bob Marley)
imo Clapton's own "Let It Grow" is No.3 with another cover - Willie and the Hand Jive (Johnny Otis) - 4th best,
Joan Jett - I Love Rock 'N' Roll - 2 best songs
Crimson and Clover (Tommy James & The Shondells )
I Love Rock 'N' Roll (The Arrows)
exactly in this order, I never particularly liked the latter but it was unavoidable in 1980s.
Santana - Abraxas - 2 best songs are covers
Black Magic Woman (Peter Green)
Oye Como Va (Tito Puente)
Bonnie Raitt - Streetlights - (at least) 3 best songs are covers
That Song About The Midway (Joni Mitchell)
What Is Success (Allen Toussaint)
Angel from Montgomery (John Prine)
actually I learned about this album only recently when I followed a lead from the Toussaint's original (I love that piano riff). I went from Dr.John⇒ Professor Longhair⇒ Toussaint⇒ this album.
UB40 - Labour of Love - a virtually whole album
Red, Red Wine (Neil Diamond)
Please Don't Make Me Cry (Winston "Groovy" Tucker)
Cherry Oh Baby (Eric Donaldson)
Many Rivers To Cross (Jimmy Cliff)
Keep on Moving (Bob Marley)
and so on........
a nice cover album actually, not exactly my cup of tea but it brings me back nicely
and now, the dessert 🥞
Cowboy Junkies - The Trinity Session - 2½ best
Sweet Jane (Lou Reed)
I'm So Lonesome I Could Cry (Hank Williams)
tied in 3rd place:
Mining for Gold (trad) and Misguided Angel (Cowboys' original)
Edit:
About being surprised, I could make a list of songs I thought were originals, but that would be off topic. This one is to all the kids who think Metallica's "Whiskey in the Jar" is the original. You googled a little and found about Thin Lizzy, right? That places the song well in this topic because it is arguably one of the best songs from "Garage, Inc. " album and it is a cover.
Well, Thin Lizzy (1972 single) version is actually a cover of Irish traditional. I was therefore not much surprised when I heard The Dubliners version (1967). Tracing back I learned that the first known recording was by Lena Bourne Fish in 1941. Lena was an elderly lady then, who died in 1945 and the song is released posthumously in 1951. You can find her version on YT titled Gilgarrah Mountain. And the biggest surprise for me was yet to follow because I stumbled upon a version by Joe Dassin titled "Mâche ta chique" (1965). It is 7 years before Thin Lizzy and in French 😮.
Edit2:
BQ2 - Coverable song. Difficult question.
Sometimes it's obvious - good catchy songs that laid forgotten for some time. Think instrumentals like Green Onions or Egyptian Reggae.
Sometimes it's exactly the opposite - musicians that rely on improvisation, like in jazz - they like to cover tunes everybody knows because the twist they bring in is more obvious than in an unknown tune. It's like when somebody makes a witty remark referring to a line from a popular movie. It's pointless if those who listen haven't seen a movie.
Sometimes a good coverable song is the one seemingly uncoverable. A sing-along song nobody can sing. But we would like we can. How many times we heard "no one can sing (play) that like...". Yet some people try and succeed. Or fail.
Example: Little Wing, Hendrix. A song we all know, few can play and sing. A dreamlike atmosphere. And dreams can be happy dreams or nightmares. Ambiguous psychedelic lyrics. Who is Little Wing? We only know from Hendrix it's "she". And there you have space for various interpretations - Clapton (painful), Sting (jazzy), Vaughan (instrumental blues)... Currently, my favorite version is a piano instrumental by Wayne Kelso (YT).
BQ - I don't mind. It's up to them.