I will now list my reasoning for why these should be in coins/how they circulated as coins:
Hard Times Tokens:
To quote the Museum of Connecticut History, “They came to be accepted as legal tender as the depression deepened and gold, silver, and, eventually, copper coins disap¬peared from circulation due to bank failures and hoarding by the public.” This shows that if they were accepted as legal tender they were there so accepted along as or equal to coins. https://museumofcthistory.org/hard-times-tokens/
Pre 1864 Civil War Tokens:
To quote the American Numismatic Association, “These cent sized tokens served as both a means of advertising for businesses and a method of payment.” This again proves they were used as payment and did circulate. These were technically legal to use until 1864, so 1863 and before have the acceptance to be considered as coins. https://www.money.org/collector/user_5712/blog/history-of-civil-war-tokens
Tax Tokens:
To quote the New York Historical Society, “Twelve states issued coin-like tax tokens, which were made of aluminum, copper, zinc, brass, plastic, fiber, cardboard, and paper.” This proves that states officially issued these, furthermore as they did circulate, they are just very low denomination state issued coins. https://emuseum.nyhistory.org/objects/53394/tax-tokens;jsessionid=C09FC42EC54787C0718EF1650E9AEFB3
Local Administration Tokens:
There are many of these. Some that local towns, cities, and even counties issued. This one is likely controversial, but it was allowed to be used in the whole county. To quote this page on Numista, “GOOD FOR 50¢ IN CASH OR TRADE AT ANY PLACE OF BUSINESS OR BANK IN
MONTGOMERY, ALABAMA ON OR BEFORE THE CLOSING OF BUSINESS FEB. 14, 1961.” This was allowed to be used at one point, so it was a coin made for circulation. N#163446
So Called Dollars:
To quote APMEX, “These were called ‘Referendum’ Dollars because even after the Election of 1896, these Dollars were circulated in Colorado.” As these were circulated it proves that they were used as coins. Other So Called Dollars did circulate and should be in the coin catalogue for that reason. https://learn.apmex.com/learning-guide/lesher-referendum-dollars-1900-1901/
Tokens/Coins from USA Western Colonies and other USA Territorial coins:
A lot of these are official issues. Brigham Young was a governor of the Utah Territory and issued coins for Utah. These coins did circulate and were official issues. To quote an article from the state of Utah, “When the coins were first circulated in St. Louis by Salt Lake merchants who used them to pay for merchandise, the $20 were accepted at $18 because of the touch of silver alloy. In the valley, however, the coins went for face value.” https://historytogo.utah.gov/doubloons/