Update 2 January 2023 Maxence Rivoir has an excellent note on the case in the CLJ here.
Lydia Lundstedt has prior review of the judgment in CJEU C-399/21 IRnova AB v FLIR Systems AB (who had been business partners in the past) here. Swedish courts are clearly busy referring the private international law elements of patent cases to the CJEU.
Of particular note is that a 3 judge chamber would seem to have ruled out reflexive effect as casually as if it were swatting a fly.
On 13 December 2019, IRnova brought an action before the Patent and Market Court seeking, inter alia, a declaration that it had a better right to the inventions covered by international patent applications, subsequently supplemented by European, US and Chinese patent applications deposited by FLIR in 2015 and 2016, and by US patents granted to FLIR on the basis of those latter applications. In support of that action, IRnova had stated, in essence, that those inventions had been made by one of its employees, meaning that that employee had to be regarded as their inventor or, at the very least, as their co-inventor. IRnova therefore argued that, as the inventor’s employer and thus successor in title, it had to be regarded as the owner of the inventions. However, FLIR, without having acquired those inventions or otherwise being entitled to do so, deposited the applications in its own name.
The court had dismissed jurisdiction viz the Chinese and US patent applications, and the US patents, on the ground, in essence, that it regarded the action concerning the determination of the inventor as being linked to the registration and validity of the patents, and it applied A24(4) BIa reflexively. The Appeals Court referred the issue on reflexive effect to the CJEU, in the following terms:
‘Is an action seeking a declaration of better entitlement to an invention, based on a claim of inventorship or co-inventorship according to national patent applications and patents registered in a non-Member State, covered by exclusive jurisdiction for the purposes of Article 24(4) of [the Brussels Ia Regulation]?’
however the CJEU reformulated [22-24] the case as not concerning reflexive effect at all, rather, enquiring about the scope of the A24(4) gateway.
The Court first of all  ff makes a point of confirming its broad reading of the ‘international’ element required to trigger European private international law, referring to CJEU Owusu.
It then  would seem to rule out reflexivity in a very matter of factly way (and as Lydia also noted, without AG Opinion) and despite as noted having earlier reformulated the question away from reflexivity:
as has already been pointed out in paragraph 26 of the present judgment, the patent applications at issue in the main proceedings were deposited and the patents concerned were granted not in a Member State, but in third countries, namely the United States and China. As Article 24(4) of the Brussels Ia Regulation does not envisage that situation, however, that provision cannot be regarded as applicable to the main proceedings.
This may have already answered a core question in BSH Hausgeräte v Aktiebolaget Electrolux.
 ff it adds (‘in any event’) reference ia to CJEU Hanssen and to the exceptional nature of A24 . It holds that 
the main proceedings relate not to the existence of the deposit of a patent application or the grant of a patent, the validity or lapse of a patent, or indeed an alleged right of priority by reason of an earlier deposit, but to whether FLIR must be regarded as being the proprietor of the right to the inventions concerned or to a portion of them.
 it refers ia to the fact that fact that
an examination of the claims of the patent or patent application at issue may have to be carried out in the light of the substantive patent law of the country in which that application was deposited or that patent was granted [however it ] does not require the application of the rule of exclusive jurisdiction laid down in Article 24(4) of the Brussels Ia Regulation
The operative part of the judgment refers both to the A24(4) restrictive interpretation element and to the third countries element hence once cannot simply regard the reflexivity issue as obiter.
Much relevant and surprisingly succinct on the reflexivity issue.
EU Private International Law, 3rd ed. 2021, 2.208 and 2.548.