Accordng to the letter your have received, you can reapply whenever you like, but you will be refused for at least the next ten years - 23/02/2026 is the date that the automatic refusal ceases to ocur, according to your above letter.
You can find the immigration rules on the offical UK government website here. The relevant sections say that (emphasis mine):
V 3.7 An applicant will be refused:
- (a) if the applicant previously breached UK immigration laws as described at V 3.9; and
- (b) if the applicant is outside the UK, the application is made within the relevant re-entry ban time period in V 3.10 (which time period is relevant will depend on the manner in which the applicant left the UK).
V 3.9 An applicant, when aged 18 years or over, breached the UK’s immigration laws:
- (d) if deception was used in relation to an application or documents used in support of an application (whether successful or not).
V3.10 (f) states that the ban for deception in an application lasts 10 years.
Note the use of the term will - there's no discretion here given to the person assessing your application, they are required to refuse you on the basis of this refusal.
If you feel you have been treated unfairly, and that you have a case to make that this was all an innocent misunderstanding and can be put right, and you really want to visit the UK, you could look into hiring a UK-based immigration lawyer. They will be able to tell you if there is any chance of you being reconsidered or not, but it will cost you a considerable amount of money.