regex101 - match all occurrences of a string only in the first line where it is found

In regex101 site I have the text:

text3 text3 text3 text3 text3 text3

text1 text2 text1 text2 text1 text2

text1 text2 text1 text2 text1 text2

text1 text2 text1 text2 text1 text2

I want to match all text2 but only in the first line where it is found:

text3 text3 text3 text3 text3 text3

text1 **text2** text1 **text2** text1 **text2**

text1 text2 text1 text2 text1 text2

text1 text2 text1 text2 text1 text2

How do I get this?

You can do this with regex flavours like PCRE, which support an end-of-match token (\G) and can be set to single line matching (/s). The idea is to match the first target by anchoring to the beginning of the line while consuming as few characters as possible (^.*?) and then to allow further matches only at the end of previous matches, while excluding line breaks in procuring them (\G[^\r\n]*?). See regex demo.

An expression to do that could look like this:

/(?:^.*?|\G[^\r\n]*?)\Ktext2/gs

\K is simply used to cut out the preceeding part of matches from the result to avoid using capturing groups for singling out text2.

To cover other aspects of line break/position matching, if you want to drop the single-line modifier (/s), in which case . ceases to match new-line characters, you can use a class that also matches line breaks, like [\s\S]*?, instead of .*? to get the initial match. See demo.

/(?:^[\s\S]*?|\G[^\r\n]*?)\Ktext2/g

If you want to use the multi-line modifier /m specifically, in which case the caret ^ now matches at the beginning of every line, you'll have to use the anchor for the beginning of string \A instead to match the initial target. See demo.

/(?:\A[\s\S]*?|\G[^\r\n]*?)\Ktext2/gm

You can do it using trick with capturing groups inside of lookahead (and disabled global flag of course).

Your regex would this:

text2(?=(?:.*?(text2))*)

Demo here

Notice that if you have more than two separate matching elements, you'll need to select .Net ending, as only it will allow multiple captures for the same group.