Yes, if unions exist at the company (which they did at Klarna), a company is required by law to negotiate with ALL employee organisations present at the company. This is one of the reasons large companies adopt kollektivavtal, it allows them to only have to negotiate with one union for employment changes.
> If the employer is not bound by any collective agreement at all, the employer is obliged to negotiate in accordance with § 11 with all relevant employee organizations in matters relating to dismissal due to a lack of work [...]
In Sweden the Unions actually makes it easier for both the workers and the company. This is a big surprise for most foreign leaders coming in unprepared for swedish culture :-)
Source (Swedish law): https://lagen.nu/1976:580#P13S2
Google translated:
> If the employer is not bound by any collective agreement at all, the employer is obliged to negotiate in accordance with § 11 with all relevant employee organizations in matters relating to dismissal due to a lack of work [...]