Not sure if this something which can be solved for JsonReader without causing backward compatibility issues.

Maybe the underlying issue here is how JsonWriter writes multiple top-level values: It just concatenates them without any separating whitespace. Not sure if that can be changed in a backward compatible way though.

Is your main use case to write multiple top-level values?
In that case a workaround (or maybe even proper solution) could be to create new JsonWriter for each top-level value (it wouldn't even have to be lenient then). However, this might cause some overhead due to all the needed new objects.

StringWriter str = new StringWriter();

while (iterator.hasNext()) {
    String value = iterator.next();
 
    JsonWriter writer = new JsonWriter(str);
    writer.setStrictness(Strictness.STRICT);
    TypeAdapters.STRING.write(writer, value);
    writer.flush();
    str.append('\n');
}

Actualy, fixing the thing on JsonReader side only is impossible i think, some cases will remain impossible to solve.
For example, a similare issue happens while writing two longs : write(1) then write(2) will produce nextLong() = 12 ...

I like your workaround, however, my case is to write and read multiple top-level values. So it is hard to implement the reading part because internaly JsonReader read into a buffer more bytes than necessary. So during the second new JsonReader(reader);, it will fail to read the next value because the inner reader has been consumed too much.

A solution in my implementation can be to write before each value an int indicating the number of bytes to read until the next value (instead of '\n'). And in the reading part, to give to JsonReader a Reader that artificially limit the number of bytes to read (by returning -1 when n bytes have been read).

Edit : Actualy using a single JsonReader with Strictness.LENIENT corretly handle multiple top level values separate by '\n'