R, 64 58 bytes

\(x){regmatches(x,t)<-Map(attr,t<-gregexpr("0+",x),"m")
x}

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Or as a one-liner:

\(x)`regmatches<-`(x,t<-gregexpr("0+",x),,Map(attr,t,"m"))

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R has some weird string manipulation functions...

R, 64 58 57 bytes

Edit: -1 byte thanks to @Dominic van Essen.

\(x){regmatches(x,t)=Map(attr,t<-gregexpr("0+",x),"m")
x}

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R has some weird string manipulation functions...

R, 64 bytes

\(x){regmatches(x,t)<-list(attr(el(t<-gregexpr("0+",x)),"m"))
x}

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Or as a one-liner:

\(x)`regmatches<-`(x,t<-gregexpr("0+",x),,list(attr(el(t),"m")))

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R has some weird string manipulation functions...

R, 64 58 bytes

\(x){regmatches(x,t)<-Map(attr,t<-gregexpr("0+",x),"m")
x}

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Or as a one-liner:

\(x)`regmatches<-`(x,t<-gregexpr("0+",x),,Map(attr,t,"m"))

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R has some weird string manipulation functions...

R, 64 bytes

\(x){regmatches(x,t)<-list(attr(el(t<-gregexpr("0+",x)),"m"))
x}

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R has some weird string manipulation functions...

R, 64 bytes

\(x){regmatches(x,t)<-list(attr(el(t<-gregexpr("0+",x)),"m"))
x}

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Or as a one-liner:

\(x)`regmatches<-`(x,t<-gregexpr("0+",x),,list(attr(el(t),"m")))

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R has some weird string manipulation functions...