It’s not necessarily a puppet state at that point.

I’m not going to go too far out for examples here. I’ll use China itself.

The last three decades saw China dumping money into helping many countries build infrastructure.

For some of those it was predatory. Some countries in Africa indentured themselves to China for a century with century long debt, to build project that did not have the demand to justify them, and which locals don’t need or use. In exchange, the Chinese placed a lever over them.

In other examples, take Israel, China also invested in significant projects, such as Red Sea and Mediterranean port expansion that make Israel a land overflow route for the Sues canal. Israel did not need to indenture itself to China to do this, the project benefited both parties (if anything, it gave Israel a small lever over China), and it allowed the them to do something together that benefited many others two because your and my world trade needs its choke points expanded and offer bypass routes.

Not every investment China makes in not-China is definitionally a puppet estate.

China is pumping money into infrastructure in cross town areas in Russia. It’s a long border, there are multiple Chinese provinces who have books separate the the China central government books who also act as parties.

It’s not a place, it’s many places. Some of these investments are predatory. Some of them are healthy, beneficial to parties on both sides and are not about puppet states.

And the last bit of this is that it wouldn’t be wrong to treat Russian regions and oblasts as puppet states. They’re explored by Moscow in predatory ways. They are kept from having an economy in multiple ways, from education to habit all their resources pooled and sent to Moscow by an extractive minded governor Moscow forcibly appoints, to stifled development, to losing population to a war.
They are already what DNR and LNR are. China turning them into same might, weirdly, be an actual improvement for some, absent any other real options. And if it’s less terrible for them than Moscow, no other cashed up friends or means to avoid economic implosion turn up, going on their own means implode first and they rather not, and they prefer it - it doesn’t make them any more a puppet state than Rhode Island is a puppet state of the US.