The recent hurricane to hit North Carolina had enormous support from ham radio as evidenced by someone who lost all power and internet: https://qrper.com/2024/11/helene-aftermath-update-insurance-.... There were many instances there of power lines not being down, but simply not existing any more.
A recently concluded event, called the CQ World Wide contest, had over 30,000 participants. A large station will make as many as 10,000 contacts in a 48 hour period exchanging basic information. Some countries call this "Radio Sport".
A US-based contest, called Sweepstakes had been going on since 1930.
A very fun event is called Field Day and takes place in June. It covers North America and participants set up emergency communication facilities as well as presenting ham radio to the public.
A recently-formed activity called Parks On The Air encourages setting up often very temporary stations in parks across the world. Activity on this is nowadays quite high with all manner of awards. See https://pota.app/ for details and index to activities.
A similar activity, called Summits on the Air (SOTA) has participants climbing peaks and putting them on the air. Some of the participants take up a challenge of building a portable station that weighs less than one pound, as some of the trails to get to the peaks require lots of hiking.
Some of the more capable hams spend significant time and energy building stations, such as K3LR: http://www.k3lr.com/. This is one of the biggest stations in the world.
One of the more significant challenges is to bounce signals off the moon and contact other hams. This is quite difficult and requires lots of RF power as well as serious antennas. The WSJTX set of protocols has made this easier, but not simple.
There are also satellites that support two-way ham radio communication. See https://www.amsat.org/ for detailed information.
There is an enormous amount of activity in building your own rigs, particularly low-powered rigs. See https://qrp-labs.com/ for example. There are many, as well as instructions on how to build them from components.
Many of these are not possible to do on the internet. For example, contacting 10,000 other stations in a 48 hour period with point-to-point communication. Or bouncing signals off the moon.
Adventurous souls often travel to nearly inaccessible locations to put them on the air. One recent example is an expedition to Bouvet https://en.wikipedia.org/wiki/3Y0J_Bouvet_Island_DXpedition. I had the fortune to go to Vanuatu in 2000 with a group from our club.
An activity that is declining in popularity is to collect contacts with US counties, of which there are 3,007 in the US. The emphasis in this is contact with mobile stations from the counties.
This is only a summary and there are many other activities and fields of interest in Ham Radio. It can simply do some things that are not feasible on the internet, and can support activities that the internet normally handles when thing go down.
If you look at K3LR's web site, you can see his support of youth.