Since the election of Peter Magyar, there have been a lot of comparisons made between him and other opposition leaders who have or are trying to unseat the ruling far-right party and are not explicitly left-wing, people like Donald Tusk in Poland or Yair Lapid and Naftali Bennett in Israel.
I don’t think these comparisons are a good fit. Peter Magyar, despite what you may have heard, is center-left.
Peter Magyar’s Platform
One of the centerpieces of Magyar’s campaign was a promise to cut taxes for those making minimum wage and below. This would be paid for by two main policies: a 1% annual wealth tax on individual wealth above 1 billion forints (about 3 million dollars), and freeing up 10 billion euros of EU development aid which was currently frozen due to corruption and rule of law concerns under Orban.
Another centerpiece of Magyar’s campaign was restoring public services that had taken a hit under Orban. He campaigned heavily on highlighting how the education and healthcare systems were in shambles under Orban.
Many of his more detailed campaign promises, explicitly called a “Hungarian New Deal” read like a left-wing wish-list:
25% pay raise for education support staff, an independent education ministry, reduced administrative burdens on teachers, restoration of university autonomy
Increase public health spending to 7% of GDP, upgrading regional hospitals
Create a new ministry dedicated to environmental protection, water management and animal welfare(!), which would have review over construction like battery plants
Double family allowances and maternity benefits, expand maternity leave, invest in elderly care facilities, and raise wages in the social sector
Investigate abuses in state child protection and compensate victims
By 2040, double the proportion of renewable energy in the energy supply
By 2030, keep air pollution below the health limits in 95% of the year
The most you can argue is that these promises, though left-wing, make Peter Magyar center-right, because Hungary is already such a right-wing place. I don’t buy this. Center-right figures don’t actively emphasize this stuff all the time like Magyar did. They don’t make really ambitious left-wing promises that they’re probably not going to keep. They make a few comments here and there promising minor left-wing policies, and mostly talk about the deficit and helping businesses. Despite this being a big theme of his post-election work, Magyar never promised to balance the budget pre-election. This was literally not a part of his campaign.
The only two right-wing policies of his I found were a promise to increase defense spending to 5% of GDP, and cut immigration by scrapping Fidesz’s migrant worker program. (He also didn’t talk about LGBT issues and refused to join the Budapest pride parade, but without any specific right-wing stance on the matter). Even there though, he argues for them the way a left-winger would: the 5% defense spending target is just a promise to abide by NATO, and the migrant worker program is being scrapped to prevent immigrants from depressing Hungarian salaries. Magyar is also aiming to replace these migrant workers with remigration of Hungarians who left the country because of Orban’s corruption, which you could argue is even more progressive, because these remigrated workers are likely to be treated better back in Hungary than other migrants would be.
Besides all this, the rest of his platform is largely broad anti-corruption promises that don’t have a specific ideological skew.
Framing
Given everything above, why is Magyar perceived as center-right?
I think the main reason is that he didn’t explicitly frame himself as left-wing. His party aligns itself with the center-right European People’s Party, he emphasized that he was a former member of Fidesz, and he framed a lot of his campaign promises like the wealth tax in an anti-corruption lens rather than a left-wing lens.
I also think immigration is a big piece. Quite frankly, it looks bad in American left-wing media circles nowadays to call someone anti-immigration left-wing. Many people’s assessment of a politician’s ideological leaning begin and end with immigration.
There are lessons to be learned from this, lessons that left-wing parties around the world desperately need to learn if they want to stave off right-wing populism. Left-wing parties should focus on fiscal issues, where their positions are more popular, rather than cultural issues. They should frame their policies in non-ideological or right-wing ways; often the policies themselves are more popular than the left-wing ideology used to justify them. And they should not to be afraid to tack right on immigration, perhaps finding creative workarounds like remigration or immigration from more palatable countries. If Peter Magyar can save a poor conservative nation from decades of right-wing governance that has ingrained right-wing policy and corruption into its very constitution, left-wing parties in Western Europe and the US have no excuse.

"Given everything above, why is Magyar perceived as center-right?"
You mentioned immigration, but I think it's social issues more broadly. Cosmopolitan pundits have a very difficult time describing someone as not right wing when they endorse a conservative status quo on issues related to gender and sexuality.