So, I'm close to the final stretch of my PhD. I have two published works and one work in progress. I've been told that I can't recycle (or I guess, simply copy/paste) the work that I've done in each of the papers in my thesis. Is this right? One of my papers has a lot of boilerplate-style introduction to a model for unfamiliar readers. So I will need to re-introduce the model in my final thesis without using the same wording (I've already used the most succinct phrasing I can come up with in the paper)?
The only valid answer for this is a local answer. Your advisor/supervisor is probably the best source. But let me mention the range of possibilities, which go from forbidden to required. It differs by both place and field.
At the required end of the scale there is the notion of the "stapled thesis" which is little more than a collection of previously published work with a bit of connective tissue to bring the body of work together. The faculty that requires this is depending on the publishing system itself to "vet" the work.
At the forbidden end (maybe too strong a term) is the notion that the thesis is a "new" work and that it treats all previous work by the author in the same way that it treats any other published work: quote judiciously and cite. Such works are often longer than typical published papers in the field, but that isn't likely to be a requirement. But they are longer since they tend to require less background from the reader and are more complete than the normal published paper.
Note that the purpose of the dissertation is to demonstrate to the faculty, and perhaps the world, that the candidate can do meaningful research in the field and can present it properly. Both the "stapled" and the "new work" versions work for this, but each faculty may have its own rules and regulation.
In the middle, there is the notion that a thesis may be considered as "something distinct" from a normal publication and the rules of scholarship might be relaxed somewhat. But how much is a matter of local custom and rules, as well as what is acceptable to the advisor.
Plagiarism notes: If you include ideas of your own from previously published work you need to cite it. This is independent of whether you copy large parts of it or not. Plagiarism is about ideas, not words. So, even when it is allowed to "include" early work, you need to cite it.
Copyright notes: Since the work is previously published you may not hold copyright anymore. This means that you need to adhere to the normal copyright rules as amended by any license you have been given by the copyright holder. It is typical, but I doubt universal, for a publisher to grant the author a license for certain uses, especially for use in a dissertation. But, there are rules and you need to adhere. It is likely that you can quote more extensively from your own published work than another person could (with citation and clear indications of what is being quoted), but there may be limitations. Look at old agreements from when the work was published or ask an editor.
And note that paraphrasing isn't an absolute guard against copyright claims. And, even paraphrasing requires citation.
At least in Spain, when you join a Ph.D. program you are subject to the regulations of that university. I don't know if in your University there is such a thing as a "doctoral administration department" (i.e. a department that is dedicated to managing the issues related to the enrollment to a Ph.D., including the rules concerning the supervision, the deposit, and defense of your thesis, etc.). If such a body exists, you could raise your issue with them.
If there is no such body, ask someone in your Department or even your supervisor. I think it unlikely that anyone on the forum knows the rules you are bound by.
"I've already used the most succinct phrasing I can come up with in the paper" there you go: as far as I know, PhD thesis having a limit on the pages number are not a common thing.
So you are good to go, you just need to be a-succinct.
Can you include the papers as chapters of the thesis (1 paper = 1 chapter)? especially in Germany it is quite common, by transparently declaring it.