English Idiom equivalent of the Tamil proverb "every house has doorsteps", meaning that everyone has problems

Nobody-is-perfect:

Used when someone's mistakes or flaws are acknowledged, to remind that everyone else makes mistakes and has flaws.

(YourDictionary)

“Into each life some rain must fall”

This quote comes from the poet Longfellow. There is a folksy but sound account of the saying in the L A Times.

The original verse from The Rainy Day:

Be still, sad heart! and cease repining; Behind the clouds is the sun still shining; Thy fate is the common fate of all, Into each life some rain must fall, Some days must be dark and dreary.

HWLongfellow

• You and me both [sister/dude]

A colloquial, sometimes jocular, slang expression that tells the listener their predicament is shared by the speaker. I believe the appendage "sister" or "dude" is more commonly said in the US.

• We're all in the same boat

Also, all in the same boat. In a similar situation, in the same position. For example, “Everyone's got too much work—we're all in the same boat.” This expression alludes to the risks shared by passengers in a small boat at sea. [Mid-1800s]
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To quote BoldBen

The expression "We all have our crosses to bear" and similar expressions means the same thing. It comes from the Christian story of the Cruxifiction where Christ had to carry his cross to the place of his execution. Over time it has somewhat softened and come to mean "we all have things we have to put up with and deal with"

The meaning of "having one's cross to bear" is confirmed at Lexico.

Have a difficult problem or responsibility one has to deal with

And the online OED (paywalled) confirms that its origin is in the bible:

A trial or affliction viewed in its Christian aspect, to be borne for Christ's sake with Christian patience; often in to bear, take (up) one's cross, with reference to Matthew x. 38, xvi. 24, etc.

"Welcome to the club"

Meaning: there are many of us in the same situation, with the same problems.