The real research will be about Ireland and the Czech Republic.
The rules for Hungary say:
who, by presenting an immunity card issued by a country listed in MFAT
Decree No. 17/2021 (V. 22.) on the unilateral recognition of immunity
certificates, certifies his/her COVID immunity and a person under the
age of 18 years under his/her supervision who enters Hungary along
with him/her;
The one thing I have never been able to answer is MFAT Decree No ...... I "know" that includes EU because I know people from the EU can cross by air with their COVID cards. Ireland is in the EU so I am guessing whatever they give you to let you into Ireland will work. But I am not sure what Ireland gives you???
who certifies that SARS-CoV-2 coronavirus was not detectable in
his/her body at the time of the study with a SARS-CoV-2 PCR test in
Hungarian or English, which is not older than 72 hours, made in a
country according to the 60/2021. (II. 12.) of the Government
paragraph 3(2a) a)-i).
If you are worried then get PCR Test.
Now, if you got to Prague first, and if you can confirm that you will have no issue crossing from the Czech Republic to Austria then I know you can cross from Austria to Hungary with NO COVID paperwork.
You can enter Hungary by road, rail and waterway from Croatia,
Austria, Romania, Serbia, Slovakia, Slovenia and Ukraine without any
epidemiological restrictions, regardless of your nationality and
coronavirus immunity, but you must have other general conditions for
entry (e.g. a valid travel document).