Tucker Carlson would appear to be wrong about this. He has been talking a remarkably pro-Putin line since the Russo-Ukrainian war heated up, and this doesn't seem to have much contact with reality.
For example, here's a story about the re-opening of the Russian stock market. It re-opened on Thursday March 24th, and rose slightly, so things are good with the Russian economy, no?
No. Foreign investors, who hold about 80% of the total shares in the Russian market, were not permitted to sell shares, at all. No short-selling is allowed, by anyone. Only a restricted list of companies, 33 blue-chip stocks by Russian standards, could be traded. This does not give any kind of truthful indication of business confidence in Russia. The Biden Administration's description of it as a "charade" seems accurate. If the sanctions weren't having an effect, these restrictions would not be needed.
Tucker Carlson has supported Putin's actions with such consistency and vehemence that a Republican political strategist suggested that he should be investigated by the Department of Justice as a "foreign asset" who is "shilling for Putin." It's not clear why he's doing this, but he is not a reliable source on this subject.
Quantifying the impact on the Russian economy of the oil and gas sanctions is difficult, because it's a moving target, with complex effects. Oil and gas exports are Russia's main source of foreign exchange, which means that their ability to import goods will be severely limited. The fall in the value of the rouble has been significant, in spite of Russian attempts to prop it up.
Update, March 31st: The rouble is now trading at levels seen before the war escalated, but this is fairly artificial:
- Base interest rates in Russia are at 20%.
- Exporters are being required to convert 80% of their foreign currency holdings into roubles.
- Foreigners cannot sell Russian securities.
- Russian residents cannot transfer money out of Russia.
All of these things create an artificial demand for roubles, and thus push up its exchange rate. They also mean that nobody would want to buy Russian securities, or convert money into roubles unless they really needed to. If these restrictions remain in place, Russia would be cut off from much of the world economy even if the sanctions ended. However, if the restrictions are removed, the rouble will fall, probably quite seriously.
When the stock market was allowed to trade all Russian stocks, but with the other restrictions described above, it unsurprisingly fell.
Russia has also threatened to require payment for its natural gas exports in roubles, but has not actually done that yet.
S&P Global Market Intelligence reckons that the Russian economy is going into its deepest recession since the 1990s, with an expected 20% fall in GDP during 2022. Since oil and gas were Russia's main exports, the loss of sales due to sanctions will be the largest cause of this.