Collaborator has shared a draft paper with a significant amount of self-plagiarism. Should I say something?

You do not need to make a fuss, or mention "plagiarism". All you need to do is to recommend adding a reference to the copied paper for each paragraph in question. That is a legitimate review comment, proposing an improvement in the draft paper.

Andreas Blass, in a valuable comment, suggests something along the lines of "The following description of our methodology is taken from [17]" or "Our methodology is the same as in [17], described there as follows" is adequate, without needing to also put quotation marks around the quoted description.

I would say something like, “I’ve noticed some reviewers/journals reacting negatively to using text from previous work verbatim. Here, I have suggested a rewrite and citation to address that potential issue.” Then actually rewrite the paragraphs in question. If the original author was copying text, they were likely trying to write the paper quickly and would appreciate that you took the time.

If the draft paper is addressing a new (though related to the previous work) research question, the background/introduction should be tailored to the new research question/objective, and as such needs to be original based on citation of a set of related previous works. However, the methodology may, for the most part, be the same as the methodology of the previously published work. In that case, it is worth stating that the details of the methodology have been published previously and to cite reference to the previous work and provide in the present paper a brief and pertinent summary of the methods. As per this editorial, "simply referencing the earlier paper" regarding the methodology may suffice, yet providing the pertinent aspects of the methods with referencing to the earlier paper may be more useful.

By and large, as per this article, if a new academic work involves some form of "text recycling" from a previous work, there is a need to clearly acknowledge that through reference citation. Besides, "...being somewhat lazy not to have attempted to rephrase/rethink previously written passages," seems worth avoiding (ibid).

However, when communicating with your collaborators about the need to avoid "self-plagiarism", you need to be wary (as pointed out by @Patricia Shanahan) not to tend to tell them that they have committed plagiarism but provide your inputs and forward your suggestions on how you feel the draft work can be improved.