AC can only go one direction
This is something the inverter's most likely doing, not your wiring
Grid-tie solar inverters are designed to feed power into an operating electric grid, and thus need a grid AC source to synchronize to.  If you deny them that grid source, they will refuse to invert.  This is to prevent the inverter from trying to power up a dead grid, which poses hazards to the linesfolk out in -20°C, 20m/s winds, and 20 cm of snow trying to get your power back on, as well as the health of the inverter.  Furthermore, grid-tie solar inverters don't have the ability to stably regulate grid frequency and voltage, or provide something called reactive power in order to keep the grid functioning properly, for that matter.
Note that if the shed is connected normally to the grid, and the grid is functional, a grid-tied solar inverter will supply power to everything: the shed, your house, and if anything is left over, up through the meter and service cable to the utility for somebody else to use.  It's doing this by synchronizing its own output to the grid-supplied AC waveform, though, hence the limitations described above.
For what you want to do, you'll need a proper inverter, not some Cheese-pipeline special, though
The bad news is that for what you're after, your inverter is likely the wrong tool for the job.  Your average cheap inverter purchased on Amazon/eBay/AliExpress/... is meant for RV(caravan)/portable power usage, and thus isn't made or tested for grid-tied service, or for long-term off-grid use for that matter.  For what you're doing, though, you need an inverter that's been independently tested to meet the applicable national/power utility standards (&quot;grid code&quot;) for interconnection to the electricity grid, even if you're running an off-grid system.  Given that you're outside North America, I would recommend a Victron MultiPlus multimode inverter.  These have good support for worldwide grid standards, extensive testing to verify that they comply with those standards, and are also going to be more rugged with regards to motor starting and such than your average cheap inverter will be.  Furthermore, they have models in the line that support 120V operation (vs. 230V), and can support off-grid operation either in addition to or instead of grid-tied service, as they have an internal switch in them that lets them automatically disconnect the inverter from the grid when mains power goes away while still providing inverter power to a set of standby loads wired to a second set of AC terminals on the inverter.