I believe the influence is hidden in countries where smaller amounts have a bigger impact.
A few million can have an outsized influence in New Zealand. Which can mean other countries interfere (not just wealthy broligarches). There was a significant controversy in the 2005 New Zealand elections regarding budgets. It is alleged US fundamentalists funded the Exclusive Brethren Church to produce pamphlets in support of the National Party, by smearing both the Labour Party and the Green Party. https://wikipedia.org/wiki/2005_New_Zealand_election_funding...
Peter Thiel was given a New Zealand passport by our National Party (maybe by being chummy, although obviously his wealth helped him). The only reason he might not influence NZ politics would be if he doesn't give a shit about our politics.
The wealthiest person born in New Zealand is Graeme Hart worth ~USD10G ranked by Forbes at about #340.
For the New Zealand 2023 General Election, political parties officially spent a total of about USD8M.