From the information you have provided, you most likely have no ban. But not having a ban does not mean you will be able to get an ESTA/visa, or be allowed to enter the US.
The ban that is relevant here is the INA 212(a)(9)(B) ban where if you accrue 180 days / 1 year of "unlawful presence" and the leave the US, you trigger a 3 year / 10 year ban, respectively. The question is whether you accrued any (and if so, how much) "unlawful presence" before you left the US. The definition of "unlawful presence" is highly technical and is what matters here.
You were in J-1 status, and people entering on J-1 are usually admitted for "D/S" (Duration of Status) on their I-94s, rather than a date. You said you believe it was "D/S" (you should check to make sure); for the purposes of this answer we will assume that it was "D/S".
The USCIS Adjudicator's Field Manual Chapter 40.9.2(b)(1)(E)(iii) deals with what can trigger "unlawful presence" to start accruing for someone in F/J/M status prior to August 9, 2018:
F, J or M nonimmigrants who failed to maintain nonimmigrant status
before August 9, 2018
F, J, or M nonimmigrants who failed to maintain their nonimmigrant
status before August 9, 2018 start accruing unlawful presence based on
that failure on August 9, 2018, unless the alien had already started
accruing unlawful presence on the earliest of the following:
• The day after DHS denied the request for the immigration benefit, if
DHS made a formal finding that the alien violated his or her
nonimmigrant status while adjudicating a request for another
• The day after the Form I-94, Arrival/Departure Record expired, if
the F, J, or M nonimmigrant was admitted for a date certain; or
• The day after an immigration judge ordered the alien excluded,
deported, or removed (whether or not the decision is appealed).
For someone who was admitted on "D/S" (not a date) on their I-94, there are only two situations that would trigger "unlawful presence" to start accruing prior to August 9, 2018: 1) you requested some immigration benefit from USCIS, and while adjudicating it, they found a status violation, and they denied the benefit you requested because of the status violation, or 2) you were in a removal/deportation hearing and an immigration judge made an order against you. From your description, it seems neither of these apply as you were never in removal/deporation proceedings, and you never applied for any benefit to USCIS during the time after your program ended, and furthermore it doesn't seem like you ever received a formal finding of status violation.
The Department of State Foreign Affairs Manual describes it similarly:
9 FAM 302.11-3(B)(1)(b)(2):
b. (U) DHS has interpreted "period of stay authorized by the Secretary
of Homeland Security" as used in this context to include:
(2) (U) For aliens inspected and admitted for "duration of status"
(DOS), any period of presence in the United States, unless DHS, IJ, or
the BIA makes a formal finding of a status violation, in which case
unlawful presence will only begin to accrue as of the date of the
9 FAM 302.11-3(B)(1)(d):
d. (U) For persons who have been admitted for duration of status (DOS)
(as is usually the case with aliens in A, G, F, J, and I visa status),
unlawful presence will not accrue unless DHS, IJ, or the BIA finds a
status violation in the context of a request for an immigration
benefit in the course of a removal proceedings. This finding of
status violation by the DHS, an IJ, or the BIA will cause a period of
"unlawful presence" to begin. In DOS cases where DHS or an IJ or the
BIA makes a formal status violation finding, the alien begins accruing
unlawful presence on the date of the finding (i.e., the date the
finding was published /communicated.
With that said, just because you don't have a ban doesn't mean you will be able to get an ESTA/visa (when you said "I'm living in a European country now, and I no longer need a visa to enter the US", you mean that your country of nationality is part of the Visa Waiver Program; but you will still need an ESTA to go to the US on VWP if you arrive by air), or be allowed to enter the US. They will likely know about your period of overstay in the US, and if asked on any form about past overstaying or violating the terms of your visa, you must truthfully say yes and provide details. With such a history of long overstay, you are very likely to be denied an ESTA or visa, or be denied entry to the US if you make it there. Even people with perfectly clean immigration histories (or no histories) are regularly denied US visas; with a history of overstay like yours, it will be even harder. However, you are free to try; it is not impossible for you to get it.