Let's try working through this. By the way, this was codified in Deuteronomy by Moses and supposedly practiced by pre-monarchy Israel in antiquity, but the specifics on how this worked out aren't well recorded.
For small businesses, loans could still be made, but would have to be done without interest. Seed money can come from personal savings and benefactors.
Mid sized businesses can also exist. The most primitive definitions of non-slave labor are like contracting: payment per some unit of measure - day of work, goods delivered, goods manufactured. To keep it rent free, the tailings would be available for the poor and strangers to pick over. Use case: the grower gets first pick at the harvest, but cannot deny access to whatever is left behind (because harvesting is generally not a 100% successful operation). The grower can not deny access to the leftovers to rot in order to protect the price of the crop - what is left behind (past a certain recognized harvest period) is considered abandoned and becomes public goods.
In practice, turning fields into public good created a crime problem as suggested in the book of Ruth - bandits would hide among the fields to ambush and abuse people trying to collect the leftovers.
As to industry - who owns the winepress I set up? It was not, in fact, uncommon in antiquity for someone to build and abandon (or gift to the community) a small piece of public infrastructure. You can probably see, however, that this will have problems scaling up from the simple well or olive press. It's not a violation of the no rent rule, possibly, for a family to personally operate their own press and insist people allow them to perform the labor for a fee.
How would trade work? If you entrust your goods to a trader to take across the continent for trade, when are those goods considered abandoned or rent? I would guess, as with infrastructure, it slips into the public good as soon as you give up working it... Therefore, families would have to cart their own goods to market.
Large industry would be possible. It could take at least two forms: large trustworthy families (think the Medicis) actively managing (and keeping control of) a widespread operation. Or, one or more investors could entrust operation of a large facility or network to a group of managers, who technically now own the piece of tooling or goods (thinking ocean-going trade ships or light factories), and can reassign (on their retirement) the goods and property to someone else. This might be done by a large wealthy family because they want to accomplish some goal : open a trade route, create a sub-assembly supplier. Auto companies have actually engaged in this in near history.
An important distinction from this rent-free society and the Medici model is that there would be no legal recognition of a patriarchy, matriarchy, or manager-of-managers. You may choose to adopt this idea or not - but to remain rent-free, I think, your society would need to consider any attempt to contractually obligate a family into in any kind of involuntary role operating on behalf of a "director" to be some sort of rent-seeking.
The key distinction here, I think, is this: no individual's legally-recognized assets may grow beyond what one human being can directly work with on a day-to-day basis.
In addition, I think you might have trouble with trade groups or prices attempting price, volume, or quality manipulation. You'd need laws governing those behaviors.
Intellectual property would need to be considered, or not exist. Without government protection of the ownership ideas you have an environment of tightly guarded trade secrets that masters regularly take with them to the grave. Perhaps government could secure an inventors ownership of an idea for some period or life (as is currently done), but require the inventors to be an active participant in the development to market and operation of the idea in order to keep the idea from slipping into the public domain.
Hotels might not exist. The primitive options for travelers were an expectation that every towns' citizens either opened up their homes for visitors (see the last chapters of Judges), or public housing was provided. Such guest houses even provided meals without charge, but you might decide they could charge for food and entertainment.
Insurance (pooling bets against actualized risk) would still be possible as an industry. Professional insurers (making their income by investing the pool) would still be possible, but the investment options would be more limited in goods and services that the insurance professional can personally take to market and sell profitably.