You're right.

A lot of this is just a mirage for multiple reasons. One of them is that emerges from the fact that the Federal Register Act of 1935 was issued in 1935 so the charts you see on mainstream news outlets almost always misleadingly start with FDR's 1st term instead of say the start of the progressive era (which is a much more coherent start date). With that broader vision you see that it's really Theodore Roosevelt instead of Franklin Roosevelt that sparks a boom in executive orders and while FDR is the most prolific the difference isn't so severe and the "number of EO per post WWII" president is a decline from progressive era-> FDR instead of a huge FDR bubble. For instance a source I mention below has their own attempted list of executive orders.

While the Progressive Era and/or FDR did see the emergence of the modern presidency (as always these things are disputed but let’s ignore that) and the rise in executive orders do somewhat illustrate that, early executive orders are also inflated because many of them issued aren’t relevant to significant policy concerns and as time moves on they’re dealt with in a more routine manner. My favorite, extremely visual and important illustration of this is the number of personal exemptions from retirement. FDR issues over 50 orders per year that are literally just “Exemption of [person name. e.g. Michael E. Gorman] from compulsory retirement for age.” That’s a little under 25% of yearly executive orders and those alone outnumber the total number of EO that Obama issued. Congressional changes to the act and EOs in 1942 (which allowed the OPM to made rulings on if specific individuals qualified for specific exemptions laid out in the EO), 1946 and 1947 pretty much reduced the use of this specific type of EO to zero (my personal digging only found Truman and JFK making one or two EO in this vein). This fits the general trend as a study by Ragsdale and Thies showed that the % of policy EO applicable to the general public went from negligible in the 1920s to over 80% in the 1980s (I’m paraphrasing Mayer’s summary from “with the stroke of a pen.” I haven’t read this specific paper). [Caveat: R&T include executive orders regarding land management as insignificant which is somewhat debatable. Most land EOs are generally as insignificant but this isn’t always the case for instance in 1996 Clinton controversially designated Grand Staircase Escalante in UT as a “national monument” to help his re-election bid].

It’s safe to say one cannot use the fact that FDR issues personal exemptions from mandatory retirement and “Obama” (or Clinton or HW or Reagan or…) doesn’t as evidence that they are being more restrained in their use of the powers of the presidency. Fundamentally cannot tell you anything useful about a specific presidents use of executive authority (especially since things counted as executive orders aren’t actually the same as “things commonly called executive orders”). Thus there is a whole literature attempting to make a “smart” count of EO by finding out the number of “significant” orders by various metrics. Annoyingly these attempted metrics often don’t play nice with each other and finding the right variables which explain prevalence of significant EOs is full of contested ground. To pick one Kenneth Mayer's attempt to classify executive orders in "with a stroke of a pen" comes up with an average of ~27 significant executive orders per year in the 1940s as opposed to 5-15 orders per year in later decades.

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I'll also throw in two generic source recommendations so that you can easily find these orders yourself if you're interested in a related question in the future.

the american presidency project http://www.presidency.ucsb.edu/ (which also includes a lot of other great data)

and

executive orders disposition tables https://www.archives.gov/federal-register/executive-orders/disposition.html