Bear in mind, joining the PTA as a member does not mean you will have to try to get to every meeting, or to any meetings. I am a member,but I do not attend PTA meetings at our daughter's school and never have - but I am the chairperson of a committee. It's fine. So don't think that you will be forced to be at meetings in the evenings or during the day when you work or whatever. A lot depends on the culture of your school and its PTA culture as well. I imagine there may be some presidents out there who are persnickety about "Well, we need you to turn out to meetings!" but in both my kid's elementary and middle schools that was not the case. PTAs usually need people to head up events, or just work on projects and events if not head them, that they cannot afford to be in a twist about who made it to meetings and who didn't.
You can participate in specific activities as you prefer, as a volunteer. You can choose to be part of the larger PTA board that plans long-term, handles a budget, talks with administrators, etc-- or not. I'm in the "or not" category. Do join officially and pay the usually very nominal dues; this allows your school PTA to report a membership number to national PTA and that does help the school PTA with resources and attention from state and national levels. But it does not mean you married PTA.
Look online or on the PTA's web page (I sure hope they have one) or wherever and find out what the subcommittees are and what specific events and initiatives they have done in the past and plan to do this year. I figure your kid is halfway through the year now but that's not too late. If you just e-mail someone who's listed as contact for, for instance, "Spring Fling field day" or whatever, and say you'd like to volunteer your time to help with it--they'll be thrilled.
PTAs do much, much more than extra fun stuff at many schools. Some use their money to pay for things like field trip costs for kids whose families cannot afford field trips, or they defray costs of instruments so that band and orchestra can be available to kids who, again, have zero money at home for instruments. Our elementary PTA paid for any kid who could not go on the four-day sixth grade camping trip, because that trip was considered high priority for that grade.
PTAs sometimes lead the way in anti-drug activities and assemblies, together with student government at higher grades. PTAs often fundraise for very big projects--the one at our elementary replaced a badly aging playground with solid, great new equipment and landscaping, which was a big expense the school could not have afforded. That was about safety as well as about fun, so it's pretty important. That PTA also had a garden club that really did amazing things with the grounds that could not have happened otherwise -- that was a case of a couple of parents who loved gardening and who came up with that idea to present to PTA. So there is a lot that PTAs do both directly with kids and by funding needed improvements. I don't know if you'd see things like the gardening as "free manual labor" but those parents devised the idea themselves and weren't told to do it by the school, and they were highly valued by the school for their initiative.
It's only a "political hot mess" if the officers make it that way. We can't say what it's like at your kid's school; you'll have to dive in and find out. Ours never were political but were pretty mellow. It's not "free manual labor for the school cutting out things and making copies" -- that kind of activity, which is really only in about grades K and maybe 1 or 2, was organized by teachers asking for parent volunteers, unrelated to PTA at all. tTeachers don't ask PTA for parent help but ask the parents of their students, in my experience.
Not sure what your school is like, but you can only find out by getting involved on whatever level works for you. If you decided you don't like PTA then do get involved in your child's classroom (that ends after about third to fifth grade depending on the teacher and by middle school, teachers do not need or really want parent volunteers except on field trips, so if you have a younger kid--get involved now.)
PTA and volunteering both keep you plugged in to what the teachers are like, how the administrators are, you get to know the "extras" teachers etc., you get to know other parents. You will be much more informed about things (including teachers your kids might have in coming years) if you participate however you can.