Basically I am using mull on android and librewolf on linux.I want to use firefox sync or something line that for syncing.So how good Firefox sync is, in privacy point on view.
I am not anonymity paranoid I just want privacy so basically what do they collect and for what?
Otherwise, i've been using Firefox Sync for years and haven't had a single issue with it.
Regarding data sharing, do note that your Firefox Account email address is shared with Troy Hunt (haveibeenpwned) via the Firefox Monitor service, so Firefox can warn you if you have suffered a data breach. Deleting your account is the only way to opt out of that. https://support.mozilla.org/en-US/kb/how-do-i-opt-out-firefox-monitor
I personally have no issue with it as he's a well known security consultant - BUT the caveat being that he's a Microsoft regional director, you couldn't know if that data is being shared any further.
As far as i know it's barely possible to really host it yourself. I don't know the details anymore but i looked into it half a year ago and quickly gave up. Think it was severely outdated and depedency issues, not sure anymore.
As others have said, it's quite good on privacy. For the truly paranoid, IIRC you can even self-host the sync server.
From the security perspective of privacy, do make sure to use a good password for the Mozilla account, the account password is also the encryption key for the E2E encryption.
Your syc data is secure, yes, but not so your account data, because is also known by Google, amon yor IP other. Enough to track you through every page with Google APIs (most) also your email, whichi is an unique identificator in the web.
Don't trust any web or service which share data to third parties, less in US webs or services.
This is one of the reason because I always prefer EU soft, webs and services. They are also not perfect respect privacy, but lightyears better as those from US companies, where something like privacy laws, GDPR and user protection don't exist or only in very deficient manner.
Technical point: US companies still need to abide by the GDPR when the user is in the EU or UK.
(But yes, I accept your main point - that protection is not shared to US citizens of those same companies who operate two very different levels of distinction. European originating software/services usually operate at the higher level of protection across all users. )
All companies that have to pay for infrastructure, servers, employees and invoices naturally need income, as is logical and legitimate. Some use contextual ads, that is, tool ads on a DIY page. This may be annoying, but it does not put privacy at risk, but if it does, when the ads are based on the user's history and data (surveillance advertising), this is what is massively used by US companies.
That there are other models to create income, for example what Proton does, with its Freemium services. The free Proton products (all of which are OpenSource, by the way), naturally have limited functions, but they do not require trafficking in user data, because they are financed through Premium services.
Andisearch, the first search engine on the market that used AI with its own language model, is strictly anonymous, no tracking or logging with sandboxed results, it is 100% free and private, for the future they plan to create a premium model for companies with specific functions for collaboration and special business functionalities, to finance the free version.
Vivaldi in new installations offers a selection of search engines (DDG, Ecosia, Startpage, etc.) and bookmarks, which pay a commission when the user uses them, if not, no, they are free to delete them, apart from a store with merch, upon insistence. from the users themselves sometime ago they also accept donations, probably also receive commissions from VAG, Mercedes, Polestar and Renault to include Vivaldi Automotive in their vehicles. All without trafficking in user data and without external investors so as not to lose independence, the mistake that Mozillla made when accepting Google as an investor. This is independent of having Google as the default search engine, since Google pays Mozilla and finances them, whether the user searches with Google or not.
It's the surveillance policy, selling user data, which is the risk and will destroy the free internet if we don't avoid it The ethics of a company respect to the user is the most important feature today, something that the big US companies don't have.
As long as Mozilla has a contract with Google, it will continue to share data with Alphabet Inc. Firefox or forks are OK, but only if you use it without the sync function, or use another provider that doesn't share the data with others.
Although Mozilla encrypts the synced data, the necessary account data is shared and used by Google to track those.
Are you saying Firefox shares data to Alphabet beyond Google as the default search engine? If so and if it applies to Sync (as if the question from OP here) can you please share sources for that?
Firefox don't share data, well, if you don't use the default Google search, but Mozilla does, sharing your account data. I hope that they finish the contract with Google, as they said, this Year.
Regarding your question: Firefox Sync is end to end encrypted, so you don't have to worry about it. It's far better than Google's browser sync, as it's encrypted at all (only in transit, but this is standard and it means that Google can still see all of your data)