shulchan aruch - response to barachu vs candles, in bringing shabbat in early?

I understand how it can be that lighting candles bring in shabbat.

But I don't understand how responding to Barachu(or any part of the davening) can bring in or be used to bring in shabbat.

I can only understand how it can work if it's only the candles that can bring it in.

If it's the candles that bring it in early, and responding to barachu that bring it in early, then the candles have to be done first, because if responding to barachu is done first, then shabbat is in and you can't light the candles.

And if responding to barachu is only ever done after the candles are lit and thus once shabbat is in, then how can responding to barachu bring in shabbat, (shabbat is already in from the candles),

I have a vague recollection once of somebody jumping up and saying not to say Barachu yet. I wonder if they said that because if he said it too early then it'd be before some people had lit the candles and thus it'd cause breaking shabbat. That suggests that it has the power to bring in shabbat but shouldn't be used to do so.

The shulchan Aruch though seems to perhaps suggest it is being used to bring in shabbat.

Shulchan Aruch 261:4

After responding to Barechu, even though it is still daytime, one may not make an eyruv nor cover over hot foods, for one has thereby already accepted /the holiness of/ Shabbos upon himself. In our times, reciting Mizmor Shir Le- Yom Ha-Shabbos 2* has the same effect as had the response to Barechu /in earlier generations/.