There used to be a battle of Fiat money with Bitcoin. There is even a large global scenario to destroy Bitcoin, this you can see almost every year there is negative news about Bitcoin. But this has nothing to have an impact on Bitcoin even now Bitcoin continues to grow. Likewise with CBDS, although many countries encourage CBDS on a large -large -scale, it will not affect Bitcoin growth.
No battle directly between fiat currency, CBDC and Bitcoin. Governments will turn their stricter regulations on Bitcoin because of many things, and not only because of their CBDCs. Money laundering, tax evasion and more reasons are there for governments to use and say as their main reasons to constrain Bitcoin but Bitcoin is strong and won't be beaten down by governments.
Because you should know that Bitcoin is created to withstand the level of inflation, interest rates are created to withstand the inflation rate.
Bitcoin itself is inflationary and we only can talk about Bitcoin deflationary after 2140 but most of us won't live till that year.
This
How is 21 million Bitcoin cap defined and enforced? writing and the chart on Bitcoin inflation vs time shows its inflationary rate with time.
Few days ago, I was reading in the news that President Trump has banned any form of creation of CBDC in the United states, if this news happen to be true which I am believing it is, it's absolutely good for bitcoin because bitcoin will remain the only dominant internet money as long as the US is concerned.
During his President propaganda months ago, he was against launch of CBDC in the USA.