Copied from my previous answer to a duplicate question:
After an extensive search, I found several other reputable articles and studies that conclusively reported a correlation between engaging in a hobby or leisurely activity and self-reported improvements in overall psychological, mental, and physical health. This includes medically reviewed reports from Harvard Medical School and the National Library of Medicine and international research studies conducted by Nature Medicine and a university research group in Lithuania.
All sources cite similarly structured data where researchers gathered information by mass distributing online or mail-in questionnaires throughout anywhere from 4 to 8 years. Nature Medicine conducted this in 16 countries, including the United States, Japan, China, and a dozen European nations. The Lithuanian university research team opted to stay more localized.
Participants would answer yes/no questions to self-report the state of their overall mood and health, and would periodically re-answer these questionnaires over time as they started and maintained a hobby or leisure activity of some sort. Some of these studies were conducted on elderly individuals, some of which had pre-existing health conditions. In contrast to those who reportedly did not participate in hobbies, those who did have a hobby reported feelings of better health and fewer symptoms linked to depression and poor mental health.
However, the majority of these sources acknowledge that these studies are purely observational data and were not met with sufficient control variables, which is a major limitation to the study's ability to conclusively connect the causality between leisure activity and psychological health, among other limitations in each study that may prevent a positive conclusion for the claim. In the words of these studies...
"[...]The study is observational and doesn't prove that hobbies caused people to be healthy and happy. But the researchers say hobbies — such as arts and crafts, games, gardening, volunteering, or participating in clubs — involve creativity, sensory engagement, self-expression, relaxation, and cognitive stimulation, which are linked to good mental health and well-being." - Harvard Medical School
"However, because these data were not assessed longitudinally after periods of stress or nonstress within person, further studies are necessary to determine whether or not these leisure activities truly restore individuals to baseline functioning after disruption by a stressful event." - National Library of Medicine
"The main limitation of our research is that it does not allow us to determine the exact causal relationship between the structure of [leisure physical activity] and health, well-being and healthy behaviour related indicators[...]" - Lithuanian graduate research group
TL;DR: Despite the extremely strong correlation between participation in hobbies and overall happiness and health, the studies used to back this claim are limited in their ability to conclude that specifically having a hobby is linked to the causation of being happier, a limitation that is credited to the fundamental downside of conducting very widespread surveys that collects self-reported data, which is susceptible to participation bias. There are a variety of other factors to consider, such as a geographical area's social culture surrounding certain hobbies, an individual's physical ability and response to certain activities, and the wide spectrum of psychological responses to any one hobby. These studies all similarly reported that while there is a correlation between hobbies and happiness, there is much more work needed to be done to supplement the current evidence to conclude the causality between the two.
Based on the results these studies report, it seems much safer to say that participating in a hobby that one enjoys may increase the likelihood of better moods and psychological health. The benefits linked to a good hobby or activity can be individually linked to positive health attributes, but the sources do not seem to be able to link an A to B causation relationship over a trickling down of positive effects that stem from good circumstances.
In short, correlation does not equal causation. For now, at least.
The human mind is a mystery indeed.
Harvard Medical School article
Medically reviewed study from the National Library of Medicine
Nature Medicine international study report
Peer-reviewed study from a Lithuanian research group
