Must an equation contain at least one variable? Can we call 1+1=2 an equation?

The definition on Wikipedia is unusual and does not match the usual usage of the term "equation" by mathematicians. Mathematicians regularly use the term "equation" to refer to any statement that two things are equal written with the symbol $=$, regardless of whether any variables are involved. It is usually used as an informal term, but can be given precise formal definitions in various settings. I do not know of any precise formal definition that requires there to be at least one variable.

I have collected different definitions from different references and tried to find out whether 1+1=2 satisfies all the conditions to be called an equation according to that definition. (The definitions and the URLs are mentioned in the question)

All of the above references except Encyclopædia Universalis can be used to call 1+1=2 an equation. Encyclopædia Universalis article mentioned about the presence of 'one or more variables' in the equality to call it an equation. But as I continued reading the article on Encyclopædia Universalis, I found another statement which can be used to contradict their definition of the equation.

An equation that is true regardless of the values ​​of the variables is an identity.

Also from Mathematics Dictionary, James and James, 5th edition, Page-147:

Equations are of two types, identities and conditional equations (or usually simply "equations")".

I think from the above 2 references, it is safe to say that identities are a subset of equations. We can call identities equation but not conditional equation (which most people simply refer as 'equation' and it should have at least one variable). We all know the famous Euler Identity ($e^{i\pi}=-1$) and it has no variable. Wolfram Mathworld and Wikipedia article mentioned Euler Identity as Euler Equation.

In mathematics, Euler's identity (also known as Euler's equation)... --Wikipedia

$e^{i\pi}+1=0$ an equation connecting the fundamental numbers i, pi, e, 1, and 0 (zero), the fundamental operations +, ×, and exponentiation, the most important relation =, and nothing else. --Wolfram Mathworld

I have also found another article, Equations And The Equal Sign In Elementary Mathematics Textbooks, written by Sarah R. Powell and was published in The Elementary school journal 2012 Jun; 112(4): 627–648. The manuscript is available on PubMed Central. They have used the following equation terminology.

A mathematical equation is an equation with zero or one variables (e.g., 9 = 6 + 3; 9 = x + 3), whereas an algebraic equation is an equation with two or more variables (e.g., x − 3 = y).

Some may argue that we can just call 1+1=2, an equality but not an equation, I shall quote the definition of Identity from the Mathematics Dictionary.

Equality: The relation of being equal; the statement, usually in the form of an equation, that two things are equal.

Thus, equality is the relation and we often express/write it as an equation. In my opinion, whether to call it an Equality or an Equation, is about English language but not about Mathematics.

_{I have also liked the Vacuous truth idea by Eric Wofsey, posted in one of the comments. 1+1=2 can also be considered as an equation in the variable x, in which x happens to not actually appear.}