Even as an EU citizen under FOM, you had to apply after 3 months.
You can apply for a Visa class D (Residence) for tourism, but you will have to prove you have medical insurance, income and attest you won't work. See https://www.nomadicmatt.com/travel-blog ... ays/#third
Nothing on that Nomadicmatt site makes me think there is any reasonably practical way of obtaining a long term tourism visa in a series of countries to allow travelling through Europe for a period of more than 3 months.
The visas referred to are residency visas and are awkward to obtain and may have various conditions attached.
It may be the case that even as an EU member state citizen strictly speaking the 3 months rule has always applied but in reality it hasn't, many northern European retirees have spent their winters in milder southern climes, many cycle tourists have spent months (more than 3) travelling throughout Europe, and as mentioned earlier, the yachting fraternity have cruised the med unhindered.
As an EU member state citizen, there was no real risk of sanction or deportation, but as a non EU member state citizen, things are very different.